N. Bodendorfer	The Verlinde formula and higher-dimensional black hole entropy Recent progress in computing black hole entropy from loop quantum gravity in higher dimensions will be reviewed. As a central result, it will be explained that the dimension of the horizon Hilbert space is computed by the Verlinde formula, independently of the number of spacetime dimensions. Counting strategies employed in 3+1 dimensions, where the Verlinde formula emerges from an SU(2) Chern-Simons theory on the horizon, are thus universally applicable.
F. Cianfrani	Generally covariant Lagrangian formulation of Relative Locality I will present a formulation of Relative Locality in curved spacetime and momentum space with manifest General Covariance. Within this scheme free particles move on spacetime geodesics and momentum dependent translations are replaced with momentum dependent geodesic deviations.
Kh. Gnatenko	Hydrogen atom spectrum in rotationally invariant noncommutative space We propose the generalization of the parameter of noncommutativity which gives the possibility to preserve the rotational symmetry in three-dimensional noncommutative space. The noncommutative algebra which is rotationally invariant is constructed. The hydrogen atom is considered in the rotationally invariant noncommutative space. We find the cor
G. Gubitosi	Finsler geometry with kappa-Poincare symmetries Finsler geometry provides a well-studied generalization of Riemannian geometry which allows to account for non trivial properties of the space of configurations of a massive relativistic particle. I show that within Finsler geometry it is possible to introduce deformations of the special relativistic mass shell compatible with kappa-Poincaré group symmetries and I discuss whether the Finsler geometry so obtained gives a description of the physical properties of a relativistic particle which is equivalent to the one emerging from the quantum group approach.
I. Kanatchikov	On precanonical quantization of gravity
P. Lavrov	A systematic study of finite BRST-BFV transformations in generalized Hamiltonian formalis We study systematically finite BRST-BFV transformations in generalized Hamiltonian formalism. We present explicitly their Jacobians and the form of a solution to the compensation equation determining the functional field dependence of finite fermionic parameters, necessary to generate arbitrary finite change of gauge-fixing functions in the path integral.
P. Naranjo	From (A)dS to Galilean (2+1)-gravity: Drinfel'd doubles and non-commutative space-times It is shown that the Drinfel'd double structure underlying the 'exotic' (2+1) Galilean and Newton-Hooke Lie algebras (with either zero or non-zero cosmological constant ?, respectively) originates as a well-defined non-relativistic contraction of a one-parameter family AdS? of relativistic Lie algebras. The underlying non-commutative space-times, along with the corresponding full quantum group structure, are analysed. [Joint work with A. Ballesteros and F.J. Herranz.]
J. Mielczarek	Loop deformations of space-time symmetries and their consequences In the Hamiltonian formulation of general relativity, general covariance is encoded in the hypersurface deformation algebra of constraints, which reduces to the Poincaré algebra in the limit of linear deformations of the hypersurace. While quantum deformations of the Poincaré algebra are a subject of intense investigations, until recently there was only very limited interest in studying quantum deformations of the more general objects, hypersurface deformation algebras. In recent years, deformations of this form have emerged from analysis of several effective models of loop quantum gravity. In the cosmological context, it has been shown that some of the quantum deformations lead to Euclideanization of spacetime at the Planck epoch and a BKL-type ultralocality. Furthermore, with use of the loop-deformed hypersurface deformation algebras, symmetries of the corresponding flat quantum spacetimes can be studied. Based on the derived loop-deformed Poincaré algebras, analysis of modified dispersion relations as well as multi-particle states can be performed. In combination with the effects in cosmology, this allows to impose observational constrains on the underlying Planck scale physics.
P. Osei	Semiduality and family of compatible r-matrices for 3d gravity The combinatorial quantisation approach to 3d gravity requires the existence of a classical rmatrix which is compatible with the classical theory, in a suitable way. However, the compatible requirement does not uniquely specify the r-matrix, leading to an apparent ambiguity in the quantisation. In this talk I will use the concept of semiduality to obtain and classify the family of compatible r-matrices, which are the classical limits of universal quantum R-matrices associated to certain quantum groups.
A. Pachol	Unified view on kappa-deformation I will provide universal formulas describing Drinfeld-type quantization of inhomogeneous orthogonal groups determined by a metric tensor of an arbitrary signature living in a spacetime of arbitrary dimension. The metric tensor does not need to be in diagonal form and ?-deformed coproducts are presented in terms of classical generators. It opens the possibility for future applications in deformed general relativity. The formulas depend on the choice of an additional vector field which parametrizes classical r -matrices. Non-equivalent deformations are then labeled by the corresponding type of stability subgroups. For the Lorentzian signature it covers three (non-equivalent) Hopf-algebraic deformations: time-like, space-like (a.k.a. tachyonic) and light-like (a.k.a. light-cone) quantizations of the Poincaré algebra.
K. Pilch	(0,2) SCFTs from the Leigh-Strassler Fixed Point We show that there is a family of two-dimensional (0,2) SCFTs associated with twisted compactifications of the four-dimensional N=1 Leigh-Strassler fixed point on a closed hyperbolic Riemann surface. We calculate the central charges for this class of theories using anomalies and c-extremization. In a suitable truncation of the five-dimensional maximal supergravity, we construct supersymmetric AdS3 solutions that are holographic duals of those two-dimensional (0,2) SCFTs. We also exhibit supersymmetric domain wall solutions that are holographically dual to the RG flows between the fourdimensional and two-dimensional theories. arXiv:1403.7131
V. Puletti	Hidden symmetries in gauge/gravity dualities The holographic principle is rigorously realized in String Theory by the so-called AdS/CFT, or gauge/gravity, duality. A key feature of the correspondence is that the gauge and string theory perturbative regimes do not overlap. This makes the correspondence on one side rather difficult to be proven, but on the other hand extremely powerful. The discovery of two-dimensional hidden symmetries, i.e. the presence of underlying integrable structures, on both sides of AdS/CFT has allowed us to reach immense progresses in understanding and confirming the duality. A natural question is whether we can extend such intricate and beautiful mathematical structures to less (super)symmetric examples of gauge/gravity duality and to observables which are fully un-protected by (super)symmetries. I will start by reviewing the main concepts of integrability in the AdS/CFT context. Then, I will discuss recent works which focus on the spectral analysis of the string world-sheet theory in AdS backgrounds, and on extending these symmetries to Wilson loop operators.
G. Rosati	Covariant Quantum Mechanics formulation of kappa-Minkowski/ kappa -Poincare I present a description of ?-Minkowski noncommutative spacetime, ?-Poincaré (Hopf-algebra) symmetry generators and relativistic-transformation parameters on a single Hilbert space. The relevant operators act on the kinematical Hilbert space of the covariant formulation of quantum mechanics, in which both time and space coordinates are quantum operators. The observable features are coded in the physical Hilbert space, obtained by enforcing the on-shellness constraint. Introducing a suitable localization operator, one can characterize "spacetime fuzziness" for particles propagating in this framework. It turns out that ?-Minkowski, also at a quantum level, presents relativity of locality, which takes the shape, in the physical Hilbert space, of a dependence of the fuzziness on the particle's energy and propagation distance.
A. Samsarov	Entanglement entropy for the noncommutative BTZ The entanglement entropy is a fundamental quantity which characterizes the correlations between sub-systems in a larger quantum-mechanical system. For two sub-systems separated by a surface the entanglement entropy is proportional to the area of the surface and depends on the UV cutoff which regulates the short-distance correlations. This naturally poses a question as to whether the entanglement entropy can account for the black hole entropy. In this talk the entanglement entropy for the noncommutative BTZ (NC BTZ) black hole shall be presented and it will be confronted with other results for the entropy of NC BTZ obtained by different approaches, particularly of that of the 't Hooft's brick wall model.
M. Samar	Relativistic particle dynamics and deformed Poincare symmetry We study the quantized spacetime Lorentz-covariant algebra proposed in [1]. This algebra contains that of Snyder as a partial case. We present the action of a relativistic particle invariant under the deformed Poincaré symmetry corresponding to the chosen algebra. It is shown that the Dirac constraint analysis of the model yields the classical version of the algebra. We also discuss algebraic transformations mapping the deformed symmetries with the undeformed ones. In the case of the considered algebra leading to Snyder's one, our results coincide with those obtained in [3]. [1] C. Quesne and V.M. Tkachuk, J. Phys. A 39 (2006) 10909 [2] H.S. Snyder, Phys. Rev. 71 (1947) 38 [3] R. Banerjee et. al., JHEP 05 (2006) 077
A. Sergyeyev	A broad new class of integrable 4D systems related to contact geometry We introduce a broad new class of dispersionless integrable systems in four independent variables having Lax pairs written in terms of contact vector fields. Our results show inter alia that integrable systems in four dimensions are considerably less exceptional than it was believed. In particular, we present a new 4D dispersionless integrable system with an arbitrarily large finite number of components. In the simplest special case this system yields a four-dimensional integrable generalization of the (2+1)-dimensional dispersionless Kadomtsev—Petviashvili equation.
R. Sverdlov	Caianello based causal set theory Causal set, proposed by Rafael Sorkin, is a model of spacetime as a partially ordered set whose elements are identified with spacetime events, and partial ordering is identified with causal relation. One of the fundamental problems of causal set theory is that it seems impossible to meet three conditions at the same time: relativistic covariance, discreteness, and locality. After all, if specetime is discrete with discreteness scale d, then relativistic covariance implies that the neighborhood of any point can be found anywhere within d-neighborhood of light cone, which, in turn, is non-local. I propose to resolve this problem in the following way: instead of viewing an element of causal set as a point in spacetime, I will view it as an element of "phase-space-time". In other words, it will have both spacetime location as well as velocity. Thus, velocity will set up "preferred frame" in which I will "cut off" the lightcone, thus restoring locality. In particular, two points can only be within a "neighborhood" of each other if they move with almost the same velocity and their coordinate displacements from each other in each of their reference frames is small. It can be argued that what I just said does not violate relativity: after all, the definition of a neighborhood based on its position does not violate translational invariance; thus, by analogy, the definition of neighborhood based on velocity should not be said to violate Lorentz covariance either.
T. Trzesniewski	Euclidean kappa-Minkowski and the Spectral Dimension kappa-Minkowski spacetime is characterized by the non-commutativity between time and spatial positions. Meanwhile, its momentum space lives on the group AN(n). The latter, in a certain sense, can be represented as (half of) the de Sitter space. A novel pre-scription for the Euclideanization of the momentum space shows that it can also be represented as (half of) the Euclidean anti-de Sitter space. This provides a curious link between the two realizations of the group momentum space. At the same time, this allows us to study the effective dimensionality of spacetime by means of the spectral dimension (which was partially explored before). Results of the corresponding calculations for three Laplacians in the (Euclidean) momentum space will be presented. This can also give us a hint for the choice of a physical Laplacian among the different proposed ones.