# TALKS IN PARALLEL SESSIONS

This page is still work in progress. Keep visiting it frequently for updates.

## MONDAY

### A. Parallel 1: Gubitosi

#### Giulia Gubitosi,

#### Jakub Mielczarek, Towards the map of quantum gravity

In this talk we will point out some possible links between different approaches to quantum gravity and models of the Planck scale physics. In particular, relations between Loop Quantum Gravity, Causal Dynamical Triangula- tions, Horava-Lifshitz gravity, Asymptotic Safety, Quantum Graphity, noncommutative geometry, deformations of the Poincare algebra and curved phase spaces models will be discussed. The relations emerge mainly from analysis of quantum deformations of the hypersurface deformation algebra, spectral dimensions, and nontrivial phase diagram of quantum gravity. We will present an attempt to arrange the observed relations in the form of a graph relating different aspects of quantum gravity. We hope that the graph (map) may turn out to be helpful in outlining a global picture of quantum gravity and will serve as an useful guide for the quantum gravity researchers.

#### Ahmed Farag Ali, Nonsingular rainbow universes

In this work, we study FRW cosmologies in the context of gravity rainbow. We discuss the general conditions for having a nonsingular FRW cosmology in gravity rainbow. We propose that gravity rainbow functions can be fixed using two known modified dispersion relation (MDR), which have been proposed in literature. The first MDR was introduced by Amelino-Camelia, et el. in [9] and the second was introduced by Magueijo and Smolin in [24]. Studying these FRW-like cosmologies, after fixing the gravity rainbow functions, leads to nonsingular solutions which can be expressed in exact forms.

#### Jose Manuel Carmona, Non-universal relativistic kinematics

We present a systematic derivation of the constraints that the relativity principle imposes between coefficients of a deformed (but rotational invariant) momentum composition law, dispersion relation, and momentum transformation laws, at first order in a power expansion of an ultraviolet energy scale. This work generalizes previous results to the case of particle-dependent relativistic kinematics, which may have interesting phenomenological applications.

#### Giacomo Rosati, Deformed relativistic symmetries in FRW spacetime

An opportunity to test Planck-scale modifications of Lorentz symmetry is represented by propagation of particles from cosmological distances (as from GRBs). DSR has been investigated so far only for flat (Minkowskian) spacetimes, providing no room for interplay with cosmological redshift. Only recently a generalization to deSitter spacetime has been proposed (Phys.Rev.D86(2012)124035), relying on the recent understanding of relativity of locality in DSR. I here propose a formulation of DSR in FRW spacetimes, discussing some of the differences with the most studied scenario for broken Lorentz symmetries.

### B. Parallel 2: Gambini / Loop Quantum Gravity

#### Rodolfo Gambini, Quantum black holes and Hawking radiation in loop quantum gravity

We introduce quantum field theory on quantum space-times techniques to characterize the quantum vacua as a first step toward studying black hole evaporation in spherical symmetry in loop quantum gravity and compute the Hawking radiation. We use as quantum space-time the recently introduced exact solution of the quantum Einstein equations in vacuum with spherical symmetry and consider a spherically symmetric test scalar field propagating on it. The use of loop quantum gravity techniques in the background space-time naturally regularizes the matter content, solving one of the main obstacles to back-reaction calculations in more traditional treatments. The discreteness of area leads to modifications of the quantum vacua, eliminating the trans-Planckian modes close to the horizon, which in turn eliminates all singularities from physical quantities, like the expectation value of the stress–energy tensor. Apart from this, the Boulware, Hartle–Hawking and Unruh vacua differ little from the treatment on a classical space-time. The asymptotic modes near scri are reproduced very well. We show that the Hawking radiation can be computed, leading

to an expression similar to the conventional one but with a high frequency cutoff. Since many of the conclusions concern asymptotic behavior, where the spherical mode of the field behaves in a similar way as higher multipole modes do, the results can be readily generalized to non spherically symmetric fields.

#### Daniele Pranzetti, CFT/Gravity Correspondence on the Isolated Horizon

A quantum isolated horizon can be modeled by an SU(2) Chern-Simons theory on a punctured 2-sphere. We show how a local 2-dimensional conformal symmetry arises at each puncture inducing an infinite set of new observables localized at the horizon which satisfy a Kac-Moody algebra. By means of the isolated horizon boundary conditions, we represent the gravitational fluxes degrees of freedom in terms of the zero modes of the Kac-Moody algebra defined on the boundary of a punctured disk. In this way, our construction encodes a precise notion of CFT/gravity correspondence. The higher modes in the algebra represent new non-geometric charges which can be represented in terms of free matter field degrees of freedom. When computing the CFT partition function of the system, these new states induce an extra degeneracy factor, representing the density of horizon states at a given energy level, which reproduces the Bekenstein’s holographic bound for an imaginary Barbero-Immirzi parameter.

#### Francesca Vidotto, Spinfoam Cosmology and Maximal Acceleration

The covariant approach of Loop Quantum Gravity (Spinfoam) has provided new insights about the quantum dynamics of the gravitational field. The task of Spinfoam Cosmology is to extract information about the dynamics of the universe directly from the full theory. I will review the basics of this framework and some recent results about the validity of the approximations utilized. In particular, I will discuss the recent realization that there is a maximal acceleration in Spinfoam and how this may be relevant for singularity resolution

#### Antonin Coutant, Unitary and non-unitary transitions around a cosmological bounce

In this presentation, we will discuss the notion of time and unitarity in the vicinity of a bounce in quantum cosmology, that is, a turning point for the scale factor. Our work follows from the Vilenkin approach to the interpretation of the solutions of the Wheeler-DeWitt equation. In this approach, unitarity is defined through the conserved current and is by nature an approximate concept. In minisuperspace it amounts to using the scale factor as a time variable. A unitary evolution is recovered when the latter becomes semiclassical enough. Unfortunately, WKB methods drastically fail near a turning point and the scale factor cannot play the role of time in scenarios with a bounce or a recollapsing phase for the universe. In this work, we extend the Vilenkin interpretation to these cases by using momentum representation. For this, we investigate the dynamics of matter transitions when using its conjugate momentum as a time. In a first part, we describe the precise conditions so as to recover unitarity, and hence, a consistent notion of probability. In a second part, we discuss a simple model in the vicinity of a bounce and present how to extend the analysis to more general models, such as Loop Quantum Cosmology.

#### Ilya Vilenskiy, Graviton Propagator and the Hessian of the Proper Vertex

The EPRL vertex amplitude provides a consistent formulation of dynamics of loop quantum gravity states. However, its semi-classical limit does not exactly match classical Regge calculus. We present a modification of the EPRL amplitude – the proper vertex amplitude – that has the correct semi-classical limit. We use the proper vertex amplitude to calculate graviton propagator and find that in semi-classical limit it agrees with the result from Lorentzian Regge calculus.

### C. Parallel 3: Sindoni / Emergent Gravity and Group Field Theory

#### Lorenzo Sindoni, Effective equations for GFT condensates from fidelity

I will describe a way to obtain the effective equations of motion for GFT condensates using the notion of fidelity. The effective equations follow from a variational principle, which can then be used instead of a truncation of the Schwinger-Dyson equations of the field theory. The same variational principle allows the assessment of the validity of the effective theory, beyond the geometric considerations that follow from the interpretation of the states in terms of homogeneous cosmologies.

#### Sylvain Carrozza, Renormalization in the Group Field Theory approach to Quantum Gravity

In this talk, I will review some recent results about the renormalization of Tensorial Group Field Theories. These theories are motivated by an approach to quantum gravity which lies at the crossroad of tensor models and loop quantum gravity. From the mathematical point of view, they are quantum field theories defined on compact Lie groups, with specic non-local interactions. Interestingly, these non-localities can be controlled and several models have now been proven perturbatively well-defined. I will especially focus on a SU(2) model inspired by Eucliden 3d quantum gravity, which has been proven renormalizable at all orders. The results will be presented from a Wilsonian renormalization group flow perspective, and special attention will be given to the conceptual and interpretational challenges of this approach.

#### Belinka Gonzàlez, Analogue gravity from fluids and the viscous case

We make a brief review of the relevant aspects and recent contributions to the field of analogue gravity, particularly concerning the fluid-gravity correspondence. We develop a specific case: a viscous, barotropic, incompressible fluid in which the flow is irrotational, though possibly time dependent. We will show that the equation of motion for the velocity potential describing an acoustic disturbance corresponds to an inhomogeneous d’Alembertian equation of motion for a minimally coupled massless scalar field, propagating in a (3+1)-dimensional Lorentzian geometry. Finally, in order to understand the energetic state of the system, we will calculate the stress-energy tensor and find it is not constant, so that there would exist energy interchange between the scalar field and the modelled space-time: the field would transfer part of its energy to increase the curvature of the space-time.

#### Alessio Belenchia, Emergent gravitational dynamics form relativistic BEC

Analogue models of gravity have played a pivotal role in the past years by providing a test bench for many open issues in quantum field theory in curved spacetime. More recently, the same models have offered a valuable framework within which current ideas about the emergence of spacetime and its dynamics could be discussed via convenient toy models. In this talk I will show that an analogue gravity system based on a relativistic Bose–Einstein condensate can, in a suitable limit, provide not only an example of an emergent spacetime (with a massive and a massless relativistic fields propagating on it) but also that this spacetime is governed by an equation with geometric meaning that takes the familiar form of the Nordstr{\”o}m theory of gravitation with a cosmological constant. The latter having an energy density naturally small, avoiding in this way the cosmological constant problem.

#### Josh Cooperman, Homogeneity measures for causal dynamical triangulations

I introduce two scale-dependent measures of homogeneity of the quantum geometry of causal dynamical triangula- tions. The first is based on the volumetric properties of the quantum geometry while the second is based on the spectral properties of the quantum geometry. Both of these measures are closely related to those used to quantify the homogeneity of our own universe on the basis of galaxy redshift surveys.

I employ these measures to quantify the homogeneity of the ensemble average quantum spacetime geometry as well as the temporal evolution of the homogeneity of the ensemble average quantum spatial geometry. I report numerical measurements for a variety of ensembles of causal triangulations. By performing a finite size scaling analysis, I attempt to extrapolate the continuum limit of these homogeneity measures.

#### Pierre Mandrin, A state occupation number prescription in the scope of minimum information quantum gravity

Conformly to [1], a quantum gravity formulation has been shown to exist on the basis of quantum number conservation, the laws of thermodynamics, unspecific interactions, and locally maximizing the ratio of resulting degrees of freedom per imposed degree of freedom of the theory. If one imposes boundary conditions on small volumes of optimized dimension (3+1), with no explicite microscopic quantum structure, Quantum Field Theory and General Relativity are recovered as special cases and all measurable quantities may be computed. Unfortunately, the number of possible states per quantum of gravity has not been specified. In this talk, a procedure for such a prescription is deduced in the scope of [1] and [2]. The procedure is shown to be compatible with well established particle occupation laws.

[1] P. A. Mandrin, Existence of a consistent quantum gravity model from minimum microscopic information, In- tern. J. Theor. Phys (2014) DOI 10.1007/s10773-014-2176-8. The final publication is available at Springer via http://dx.doi.org/10.1007/s10773-014-2176-8.

[2] P. A. Mandrin, Spin-compatible construction of a consistent quantum gravity model from minimum information}, Poster presented at the Conference on Quantum Gravity, “Frontiers of Fundamental Physics 2014″, Marseille, 15-18 July (2014).

## TUESDAY

### A. Parallel 1: Calcagni / Shape Dynamics and Loop Quantum Gravity

#### Gianluca Calcagni, Cosmology and quantum gravities: Where are we?

Abstract: We review the status of various quantum gravity theories regarding the main problems of modern cosmology: the big bang, the cosmological constant, the nature of inflation and of dark energy, and the existence and role of higher- order curvature corrections in the gravitational action. Special attention is given to causal dynamical triangulations, asymptotic safety, loop quantum gravity, group field theory, causal sets and emergent gravity, discussing how these theories can justify phenomenological models and how actual cosmological predictions could be extracted in the near future.

#### Francesco Cianfrani, Introduction to Quantum-Reduced Loop Gravity

I will give a review of Quantum Reduced Loop Gravity and of its recent achievements in founding Loop Quantum Cosmology.

#### Emanuele Alesci, Quantum Reduced Loop Gravity

Quantum Reduced Loop Gravity is a recently proposed model to address the quantum dynamics of the early Universe. We will review it’s semiclassical limit, a link with LQC and how the QRLG could simplify the analysis of the dynamics in the full theory.

#### Henrique Gomes, Conformal Geometrodynamics regained: gravity from duality

There exist several ways of constructing general relativity from ‘first principles’: Einstein’s original derivation, Lovelock’s results concerning the exceptional nature of the Einstein tensor from a mathematical perspective, and Hojman-Kucha\v r-Teitelboim’s derivation of the Hamiltonian form of the theory from the symmetries of spacetime, to name a few. Here I propose a different set of first principles to obtain general relativity in the canonical framework without presupposing spacetime in any way. I first require consistent propagation of scalar spatially covariant constraints. I find that up to a certain order in derivatives (four spatial and two temporal), there are large families of such consistently propagated constraints. Then I look for pairs of such constraints that can gauge-fix each other and form a theory with two dynamical degrees of freedom per \emph{space} point. This demand singles out the ADM Hamiltonian either in i) CMC gauge, with arbitrary (finite, non-zero) speed of light, and an extra term linear in York time, or ii) a gauge where the Hubble parameter is conformally harmonic.

#### Sean Gryb, The Role of Symmetry in Shape Dynamics and Some Applications

After reviewing the basics of Shape Dynamics, we will discuss the physical meaning of the claimed duality to General Relativity. We find that it is perhaps more appropriate to think of conformal invariance as a “complimentary” or “hidden” symmetry to those of General Relativity, rather than a strict duality. We then make use of this insight to shed new light on asymptotically flat formulations of Shape Dynamics, and study thin shell collapse in this framework.

#### Andrea Napoletano, On compact, spherically symmetric solutions of Shape Dynamics

In my talk, I will discuss the spherically symmetric solutions of the equations of Shape Dynamics in a compact manifold. First I will show how to implement the hypothesis of spherical symmetry and then analyze the solutions. They can be classified in terms of a first integral of motion and I’m going to show how they lead to very different scenarios. Finally I will contextualize these results in the more general background of Shape Dynamics to contribute to the delineation of a general coherent picture.

#### Riccioni

#### Bochicchio

#### Marrani

#### Condeescu

#### Rosseel

### B. Parallel 2: Riccioni / String Theory

### C. Parallel 3: Urrutia / Altera

#### Marc Holman, The Significance of Empirical Principles for Quantum Gravity

In recent work (SHPMP 2014, 46, 142-153; arXiv : 1308.5097) I singled out four empirical principles that should arguably pay a key role in retrieving the principles of a missing theory of “quantum gravity” — i.e., an even-handed theory that consistently unifies the principles of quantum theory and general relativity — namely (i) quantum nonlocality, (ii) irreducible indeterminacy, (iii) the thermodynamic arrow of time and (iv) the CMB uniformity.

In this 20-minute compressed presentation I will go into the deeper historical and conceptual motivations behind this approach and, time permitting, also discuss why, in my view, current mainstream theoretical ideas fall short at succesfully incorporating the principles in question.

#### Igor Kanatchikov, On precanonical quantization of gravity

In the talk I would outline an approach to quantization of gravity which I call precanonical quantization (the reasons will be explained). It is based on a hamiltonization of field theory, known as the De Donder – Weyl theory, which does not require splitting into the space and time, as the canonical hamiltonian formalism does. I will outline the mathematical structures of DW theory, which are relevant for quantization (found in my earlier works), use them for quantization of a nonlinear scalar field, as a simple example, and show how the resulting formulation can be related to the standard QFT (so that the latter appears as a limiting case of vanishing “elementary volume of space”, which enters the theory when quantized differential forms are represented by Clifford algebra elements). Then I will use this framework to quantize General Relativity precanonically. On the way I will have to use a generalization of the Dirac’s contraints theory to the DW hamiltonian formulation in order to find the fundamental (generalized Dirac) brackets. This approach to quantization leads to an essentially nonperturbative formulation which is not plagued by the mathematical difficulties related to the infinite dimensional functional spaces, as in the canonical formulation. One of the consequences of the resulting formulation is that quantum geometry of space-time is described in terms of transition amplitudes between the values of spin-connection at different points of space, which in principle can be calculated from the equations of precanonical quantum gravity, which we derive. I also will discuss a simple application of the approach to quantum cosmology.

#### Philipp Höhen, Quantum formalism for systems with temporally varying discretization

A canonical quantum formalism for discrete systems subject to a discretization changing dynamics is outlined. This framework enables one to systematically study (non-)unitarity of such dynamics, the role of canonical constraints and the fate of Dirac observables on temporally varying discretizations. It will be illustrated how the formalism can also be employed to generate a vacuum for a scalar eld on an evolving lattice. Implications for the dynamics in simplicial quantum gravity models are commented on.

#### Fabio Costa, Non-classical causal relations

A classical, causal, space-time enforces a well-defined direction of causal relations: If an event A is a cause for an event B, B cannot be a cause of A. However, this might not be true at a more fundamental level, where space-time might lose its classical properties. We explore such a possibility by setting out a general formalism that descibes all possible scenarios where, locally, physics is described by quantum mechanics, but no global causal structure is assumed. In this formalism, there exist signalling correlations that are incompatible with any underlying causal structure. I will briefly discuss to what extent such correlations might be identified with possible quantum properties of space-time.

#### Stefan Lippoldt, Fermions in gravity with local spin-base invariance

We study a formulation of Dirac fermions in curved spacetime that respects general coordinate invariance as well as invariance under local spin-base transformations. The natural variables for this formulation are spacetime-dependent Dirac matrices subject to the Clifford-algebra constraint. In particular, a coframe, i.e. vierbein field is not required. This is of particular relevance for field theory approaches to quantum gravity, as it can serve for a purely metric-based quantization scheme for gravity even in the presence of fermions.

#### Mario Herrero Valea, Conformal matter and gravitation

Conformal symmetry in the presence of gravitation is translated onto Weyl invariance. Conformal dilaton gravity is a particular model in which the Weyl gauge field has vanishing field strength and can be represented through the derivative of a scalar field. Some models of invariant matter related to this are studied and the difference between dynamical and non-dynamical gravity is emphasized with the aim of understanding the quantum fate of conformal symmetry.

#### Arif Mohd, Asymptotic symmetries of massless QED and the soft-photon theorem

By analyzing the radiative phase space of massless QED at null-infinity, I will provide a systematic derivation of a recent result of Strominger et al that Weinberg’s soft-photon theorem is the Ward identity corresponding to a symmetry of the S-matrix. The symmetry in question is a diagonal subgroup of the gauge transformations which do not die at the future and past null infinity.

#### Ghaliah Alhamzi, From homotopy to ITO calculus

We begin with a deformation of a differential graded algebra by adding time and using a homotopy. It is shown that the standard formulae of It\^o calculus are an example, with four caveats: First, it says no thing about probability. Second, it assumes smooth functions. Third, it deforms all orders of forms, not just first order. Fourth, it also deforms the product of the forms. An isomorphism between the deformed and original differential graded algebras may be interpreted as the transformation rule between the Stratonovich and classical calculus (again no probability).

### D. Parallel 4: Martinetti / Non Commutative Geometry

#### Pierre Martinetti, Non-commutative geometry and quantum gravity

From the early intuitions of Bronstein in the 30’ till the most recent models of quantum spacetime, research in quantum gravity strongly suggests that geometry at the Planck scale cannot be described by (pseudo)-Riemannian geometry. Non-commutative geometry is a proposal to extend the usual tools of differential geometry in such a way to encompass both gravitational and quantum effects. We shall give a brief overview of applications of non-commutative geometry to quantum gravity, like spacetimes with deformed Lorentz symmetry, the Doplicher-Fredenhagen-Roberts quantum spacetime, or Connes description of the standard model coupled to gravity.

#### Agostino Devastato, Non-commutative geometry, symmetry breaking and Higgs mass

In the context of the spectral action and the noncommutative approach to the standard model we describe some applications to the particle physics world. In particular we will present the main topics of the non-commutative geometry approach showing how it is possible to obtain a prediction of the Higgs mass.

#### Valerio Astuti, Covariant quantum mechanics applied to noncommutative geometry

In this talk I will give a brief review of the covariant quantum mechanics formalism and its application to non-commutative spacetimes. In particular I will show that the most natural environment in which to define nontrivial commutation rules between coordinates is the so called kinematical Hilbert space, which is just a gateway to the physical properties of a theory. In this space it is easy to give a representation of noncommutative spacetimes with particle dynamics which in the commutative limit reduce to the standard quantum mechanics.

#### Stefano Bianco, The DSR-deformed relativistic symmetries and the relative locality of 3D quantum gravity

Over the last decade there were significant advances in the understanding of quantum gravity coupled to point particles in 3D (2+1-dimensional) spacetime. Most notably it is emerging that the theory can be effectively described as a theory of free particles on a momentum space with anti-deSitter geometry and with noncommutative spacetime coordinates of the type [x^\mu, x^\nu] = i \hbar 4 \pi G \varepsilon^{\mu\nu}_\rho x^\rho. We here show that the recently proposed relative-locality curved-momentum-space framework is ideally suited for accommodating these structures characteristic of 3D quantum gravity. Through this we obtain an intuitive characterization of the DSR-deformed Poincar \’e symmetries of 3D quantum gravity, and find that the associated relative spacetime locality is of the type producing dual-gravity lensing.

#### Giovanni Palmisano, On relativistic curved momentum spaces

We discuss an implementation of the relativistic principle on curved momentum spaces and some features regarding the geometrical structure of the momentum spaces admitting such an implementation.

## THURSDAY

### A. Parallel 1: Martinetti / Non Commutative Geometry

#### Latham Boyle, Non-commutative geometry, non-associative geometry, and the standard model of particle physics

Connes’ notion of non-commutative geometry (NCG) generalizes Riemannian geometry and yields a striking rein- terepretation of the standard model of particle physics, coupled to Einstein gravity. We suggest a simple reformu- lation with two key mathematical advantages: (i) it unifies many of the traditional NCG axioms into a single one; and (ii) it immediately generalizes from non-commutative to non-associative geometry. Remarkably, it also resolves a long-standing problem plaguing the NCG construction of the standard model, by precisely eliminating from the action the collection of 7 unwanted terms that previously had to be removed by an extra, non-geometric, assumption. With this problem solved, the NCG algorithm for constructing the standard model action is significantly tighter and more explanatory than the traditional one based on effective field theory.

#### Shane Farnsworth, The standard model of particle physics from non-commutative geometry: new symmetries, new predictions, and a new solution to the Higgs mass problem

L. Boyle’s talk described a reformulation of Connes’ non-commutative geometry (NCG), and some of its consequences for the NCG construction of the standard model of particle physics. In this talk, we describe several further conse- quences. In particular, the new formulation predicts an extra spontaneously broken U(1)_{B-L} gauge symmetry and, relatedly, a new complex Higgs field which carries B-L charge. In addition to resolving the Higgs mass problem which had plagued non-commutative geometry, this field has important cosmological implications.

#### Luca Tomassini, Non-commutative spacetimes, fields and quantum gravity: some news from DFR

We present some recent results and ongoing work in the study of cosmological spacetimes in the framework of the DFR (Doplicher-Fredenhagen-Roberts) approach to non-commutative spacetime. We present physically motivated uncertainty relations for coordinates of expanding Friedmann flat spacetimes and corresponding non-commutative objects whose commutation relations grant that they are satisfied. This allows the construction of quantum fields and thus of quantum energy momenum tensors. Finally, a quantum version of the Friedmann equations will be discussed.

#### Max Kurkov, High momenta bosons do not propagate

Bosonic Spectral action coming from noncommutative geometry successfully describes the Standard Model coupled with gravity and has a predictive power. Standard approach to this is based on the asymptotic heat kernel expansion, which is suitable for low energy region, but does not capture the high momenta behavior. On the other side one can try to use noncommutative geometry and the spectral action to investigate the early universe, and try to infer something related to physics near the quantum gravity transition. Using the Barvinsky-Vilkovisky expansion, suitable for high momenta region we compute high momenta asymptotic of the bosonic spectral action and find that it vanishes at high momenta. We interpret this as the fact that the two point Green functions vanish for nearby points, where the proximity scale is given by the inverse of the cutoff.

### B. Parallel 2: Eichhorn / Asymptotic Safety and Dimensional Reduction

#### Astrid Eichhorn, Spectral dimensions of quantum spacetime

I will introduce the spectral dimension, which is a notion of dimensionality that a probe particle, diffusing on a quantum spacetime “sees”. I will discuss how to properly construct candidate diffusion equations to describe this process in asymptotically safe quantum gravity and Horava-Lifshitz gravity, which show dynamical dimensional reduction at very high momenta. Finally, I will show how to derive the spectral dimension in a Lorentzian approach to quantum gravity, namely causal set theory. In that case, the Lorentzian nature of quantum spacetime leads to a surprising new feature, namely a dimensional growth at small length scales.

#### Dario Benedetti,

#### Tugba Buyukbese, 1/D expansion for quantum gravity

Large-N techniques, where N denotes the dimensions of the local gauge symmetry, are very powerful tools in the study of strongly interacting quantum fields. In gravity, the role of N is taken by the number of space-time dimensions D. We discuss the 1/D expansion for quantum gravity using functional renormalisation. We find that the theory displays an asymptotically safe UV fixed point, and that the 1/D expansion has a finite radius of convergence down to around D = 22 dimensions. Implications of the results are discussed and compared with earlier findings based on perturbation theory and effective field theory.

#### Kevin Falls, Asymptotic safety and physical degrees of freedom in quantum gravity

We study the renormalisation group flow of gravity in four dimensions. Revisiting the Einstein-Hilbert approximation we consider the physical degrees of freedom and the role of the cosmological constant. At the level of the flow equation we make manifest the propagating and topological degrees of freedom by taking care to properly treat the functional measure. In addition we implement the regulate in such a way as to ensure convexity of the effective action while closing the approximation via a truncation of the early time heat kernel expansion. The resulting phase diagram possesses a UV fixed point with real critical exponents and a classical IR limit. At one-loop we find the critical exponents are independent of the regulator function.

#### Rachwal, Super-renormalizable and Finite Gravitational Theories

We introduce and extensively study a class of non-polynomial higher derivative theories of gravity that realize a ultraviolet (UV) completion of Einstein general relativity. These theories are unitary (ghost free) and at most only one-loop divergences survive. The outcome is a class of theories super-renormalizable in even dimension and finite in odd dimension. Moreover, we explicitly prove in D=4 that there exists an extension of the theory that is completely finite and all the beta functions vanish even at one-loop. These results can be easily extended in extra dimensions and it is likely that the higher dimensional theory can be made finite too. Therefore we have the possibility for “finite quantum gravity” in any dimension.

### C. Parallel 3: Gubitosi

#### Salvatore Mignemi, Relativistic dynamics of Snyder space-time

We study the classical dynamics of a particle in Snyder spacetime, adopting Dirac’s formalism of constrained Hamilto- nian systems. A remarkable result is that in the relativistic Snyder model a consistent choice of the time variable must necessarily depend on the dynamics. This is a consequence of the nontrivial mixing between position and momentum intrinsic to the model.

#### Christian Pfeifer, Finsler geometry as geometry of spacetime: The Finsler spacetime framework

Finsler geometry is a long known generalisation of Riemannian metric geometry and there are numerous attempts to apply it as geometry of spacetime in physics. However there appear severe problems in the standard formulation of Finsler geometry when it is used as generalisation of indefinite Lorentzian metric geometry due to the existence of non-trivial null directions. In this talk I present the Finsler spacetime framework which overcomes these problems and makes Finsler geometry available as generalisation of Lorentzian metric geometry and thus as geometry of spacetime. I begin with a short review of Finsler geometry and the problems with non-trivial null directions in its standard formulation before I present our definition of Finsler spacetimes which overcomes these issues. Afterwards I discuss that Finsler spacetimes serve as geometric backgrounds for physics as well as Lorentzian metric spacetimes, from the point of view that they realise the three-fold role of the geometry of spacetime in physics: a clear geometric notion of causality, observers and their measurement and the description of gravity.

#### Niccolò Loret, DSR-relativistic symmetries in Finsler geometries

Finsler geometry provides a well studied generalization of Riemannian geometry which allows to account for possi- bly non-trivial structure of the space of configurations of a massive relativistic particle. Another recently developed framework for the description of modified relativistic particle kinematics relies on the description of the particle momentum-space as a curved (pseudo-Riemannian) manifold. We will show that in some cases these two frame- works give equivalent descriptions of the physical properties of a relativistic particle, when its momentum-space is characterized by a deSitter metric and the spacetime is flat. The generalization of this result could provide a useful mathematical tool to formalize Deformed Special Relativity phenomenology to curved spacetimes.

#### Orchidea Maria Lecian, Non-trivial Momentum-Space structures for General Relativity: a quantum approach

The compatibility of the definition of non-trivial momentum-space structures in the realization of the quantum regime for General Relativity: a quantum deformation of the topology of the physical spacetime is investigated to be com- patible with the definition of an algebraic manifold defined by the gauge-invariance of a deformed Poncaré algebra.

#### Tomasz Trzesniewski , Conical Defects and Curved Momentum Space

Codimension 2 conical defects in the classical gravity are quite simple objects and therefore can easily provide some insight into the fundamental features of gravitation in any dimension. The most interesting are timelike and lightlike (massless) defects, where the latter can be obtained by boosting of the former. The point which have not been stressed before is that in de Sitter spacetime every defect can be considered a direct projection of the 1-dimension- higher defect in the embedding Minkowski spacetime. Meanwhile, a conical defect in the Minkowski spacetime can be completely characterized by the holonomy of a loop around it. For massive defects the holonomy is an elliptic Lorentz transformation while for massless defects it is a parabolic one. Parabolic (or null) rotations “around” a given direction, together with the perpendicular boosts, form the abelian nilpotent group AN(n), which parametrizes massless defects. This group is also the momentum space of non-commutative kappa-Minkowski spacetime, which provides a curious link between the latter and conical defects.

#### Andrea Dapor, Lorentz Violation in Quantum Cosmology

I will present a new perspective on QFT on quantum cosmological space-times. The standard approach to extract the semiclassical limit of a quantum theory consists in taking the expectation value of observables on a semiclassical state. In the case of quantum cosmology, this procedure produces an effective classical metric (which in general does not obey Einstein’s field equations). I show that, once quantum matter is put in the game, a new possibility arises: the dynamics of matter on quantum space-time can be equivalently described by standard QFT on a classical space-time, whose geometry is encoded in an effective classical metric which is different than the standard semiclassical one. Such matter-dependent effective metric can be thought of as the metric “seen” by the matter field. In particular, if the matter is a scalar field with non-vanishing potential (such as the inflation field), then the effective metric depends on the energy of the quanta of the scalar field, and the dispersion relation is thus modified. This leads to an apparent violation of Lorentz symmetry which might be detectable in GRB observations, or might have played a role in the very early Universe. The results I will present are based on Phys.Rev. D 86 (2012) 064013 and Phys.Rev. D 87 (2013) 063512, but consist mostly of material yet unpublished.