Foundations and mathematical aspects of gravity theories:

Andrea Addazi, Fudan University: Topological M-theory and Loop Quantum Gravity: S-branes and Space-time foam

we show two curious coincidences which may shine light on a new correspondence principle between Loop Quantum Gravity and M-theory, in certain kinematical regimes. First, the low wave-lenght limits of topological M-theory on G2 manifolds can re-construct the $3+1$ gravity in self-dual variables formulation. Second, we argue that non-trivial gravitational holonomies correspond to a class of Space-like M-branes (SM-branes). Can that suggest "a new duality" among the two so different candidates of quantum gravity?

Yannick Herfray, Ecole normale superieur de Lyon: 3D and 4D gravity from 3-forms in 6D and 7D

In arXiv:1605.07510, arXiv:1705.01741 and arXiv:1705.04477 we studied the dimensional reduction of a certain theory of 3-forms due to Hitchin from 6D and 7D to 3D and 4D. The resulting theories turns out to be pure gravity for the 3D case and some modified theory of gravity coupled with other fields in 4D. We will briefly review Hitchin theory of stable forms and describe the resulting dimensional reductions.

Florian Hopfmueller, Perimeter Institute, Waterloo, ON, Canada: Metric Gravity Degrees of Freedom on a Null Surface

A canonical analysis for metric general relativity is performed on a null surface without fixing the diffeomorphism gauge, and the canonical pairs of configuration and momentum variables are derived. Next to the well-known spin-2 pair, also spin-1 and spin-0 pairs are identified. The boundary action for a null boundary segment of spacetime is obtained, including terms on codimension two corners.
F. Hopfmüller and L. Freidel, Phys. Rev. D 95, no. 10, 104006 (2017), arXiv:1611.03096

Maciej Kolanowski, University of Warsaw: Null observables and deformed Poincare symmetry

Introduction of physical observator is one of possible approaches to the problem of observables in general relativity. Construction of such observator (and associated coordinates) using null geodesics will be given. Possible obstruction against their existence will also be discussed together with some physical examples. Transformations between such frames can be thought to form, in some suitable sense, Poincare group deformed by curvature. Explanation of the exact meaning of this statement will be followed by more detailed analysis of the obtained structure. The talk will be concluded by the comparison between these symmetries and Bondi-Mertzner-Sachs group.

Isha Kotecha, Albert Einstein Institute: Statistical Equilibrium in Group Field Theory

The issue of defining statistical mechanics in a covariant setting is well-known. A group field theory is inherently covariant, with no a priori preferred time variable. This translates to no preferred Hamiltonian defined for the system, and hence no conventional notion of equilibrium a la Gibbs. In this talk, I will discuss our investigation into defining equilibrium for a quantum group field theory system. It has been realised that the relevant Hilbert space of spin networks of arbitrary number of nodes (each with an arbitrary but fixed valency) can be given in the form of a Fock space. Using this representation of the GFT Weyl algebra, we define states which are at equilibrium with respect to certain automorphisms of the same algebra. These are the Gibbs states which we find are the unique KMS states for these automorphisms. Such states are fundamentally distinct from the standard ones in the sense that they define equilibrium with respect to internal parameters.

Suzanne Lanéry, Centro de Ciencias Matemáticas, Universidad Nacional Autónoma de México, Morelia, Mexico: Projective State Spaces for Quantum Field Theory and Quantum Gravity

Instead of formulating the states of a Quantum Field Theory (QFT) as density matrices over a single large Hilbert space, it has been proposed by Kijowski to construct them as consistent families of partial density matrices, the latter being defined over small 'building block' Hilbert spaces. In this picture, each small Hilbert space can be physically interpreted as extracting from the full theory specific degrees of freedom (aka. 'coarse-graining' the continuous theory). This allows to reduce the quantization of a classical field theory to the quantization of finite-dimensional sub-systems, while obtaining robust and well-controlled quantum states spaces.
I will present new results obtained in this framework, and discuss its benefits eg. for connecting canonical and covariant approaches to exploit their respective strengths, or for investigating the classical regime of background-independent Quantum Gravity.

Pierre Martin-Dussaud, ENS Lyon: Asymptotics of Lorentzian polyhedra propagator revisited

We revisit and extend Jack Puchta’s large spin analysis of the propagator for the Lorentzian EPRL model. In particular, we compare its method with the spinorial methods more commonly used in spin foam asymptotic, and discuss subtle aspects of the approximation, its numerical confirmation, and more importantly its extension to the non-diagonal case which is crucial to restore non-trivial dihedral angles.

Prince Osei, Perimeter Institute for Theoretical Physics: Title: Quaistriangular structure and twisting of the 2+1 bicrossproduct model

We show that the bicrossproduct model quantum Poincare group in 2+1 dimensions acting on the Majid-Ruegg quantum spacetime model is related by a Drinfeld and module-algebra twist to the quantum double acting on the spin quantum spacetime model. We obtain this twist by taking a scaling limit as q--> 1 of the q-deformed version of the above where it corresponds to a previous theory of q-deformed Wick rotation from q-Euclidean to q-Minkowski space. We also recover a twist known at the Lie bialgebra level. Our method is general and applies to all compact real forms of complex simple groups and to the quantum group case.

Carlos I. Perez Sanchez, Mathematics Institute, University of Münster: Corrrelation functions of colored random tensors and their Schwinger-Dyson equations

Tensor models are a random geometry framework that generalizes, to arbitrary dimension, matrix models. They are used to model quantum gravity but, lately, also some applications to AdS/CFT were discovered. Colored tensor models are the orientable geometry sector of tensor models. We scrutinize the correlation functions of colored tensor models and give briefly their geometric interpretation in terms of bordisms. Based on a Ward-Takahashi identity, we give the Schwinger-Dyson Equations they obey. We proceed non-perturbatively.

Matti Raasakka, Independent researcher: Finite-dimensional Local Quantum Physics and Spacetime Structure

Local Quantum Physics (and its generally covariant generalization) provides a rigorous way to define quantum field theories (QFTs) on arbitrary globally hyperbolic spacetimes by assigning observable algebras to local spacetime regions. For QFTs, the local observable algebras are known to be infinite-dimensional, while physical considerations (e.g., the finiteness of black hole entropy) seem to suggest that, at the fundamental level, finite local spacetime regions carry only a finite number of degrees of freedom, and therefore should be assigned finite-dimensional observable algebras. This motivates the study of finite-dimensional models in the framework of Local Quantum Physics.
In this talk, I discuss the formulation and the physical interpretation of finite-dimensional models in Local Quantum Physics, and their implications for spacetime structure. In particular, I show that local Lorentz covariance follows from the assumption that the vacuum is in equilibrium on minimal local observable algebras isomorphic to the algebra of 2-by-2 complex-valued matrices, i.e, the observable algebra of a single qubit. This result provides a direct relationship between the microscopic structure of the quantum vacuum and spacetime geometry: The connection between local inertial reference frames can be extracted by comparing the local restrictions of the vacuum state. Hopefully, this observation will lead to an improved understanding of the interplay between quantum physics and spacetime structure.
The talk is partially based on the preprint arXiv:1705.06711.

Robert Seeger, Friedrich-Alexander-Universität Erlangen-Nürnberg: Towards Gaussian states for the holonomy-flux algebra

Quasifree states are very important in standard QFT, since they contain the Fock states. As a toy model, we consider the U(1) holonomy-flux algebra. We show that it is a Weyl-algebra and consider quasifree states for it. (They have to be diffeomorphism non-invariant due to uniqueness theorems). We find a new class of states that are “almost quasifree” in the sense that they are Gaussian for the electric flux, but similar to the Ashtekar-Lewandowski state for holonomies. We show an example that, curiously, involves states of the harmonic oscillator. We also discuss necessary conditions for true quasifree states, and the extension of our results to SU(2).

Daniel Siemssen, University of Warsaw: Feynman propagators and the self-adjointness of the Klein-Gordon operator

I will discuss the construction of Feynman propagators for the Klein-Gordon equation on curved spacetimes. It is generally accepted that there exists no preferred Feynman propagator on curved spacetimes. However, in some cases a distinguished choice may exist. This is related to some curious open problems related to the self-adjointness of the Klein-Gordon operator.

Tatjana Vukasinac, : Weakly isolated horizons and Holst action

Weakly isolated horizons are quasilocal generalizations of event horizons and their definition is purely geometrical, and independent of the variables used in describing the gravitational field. On the other hand, the formulation of an action principle and its corresponding Hamiltonian formulations is very sensitive to the choices of variables and boundary terms. With an eye towards a canonical formulation we consider general relativity in terms of connection and vierbein variables and their corresponding first order action, the Holst action. We focus on the role of the internal gauge freedom that exists, in the consistent formulations of the action principle.