General Relativity & Quantum Cosmology

In this talk, I will describe the framework of large D matrix models, which provides new limits for matrix models where the sum over planar graphs simplifies when D is large. The basic degrees of freedom are a set of D real matrices of size NxN which is invariant under O(D). These matrices can be naturally interpreted as a real tensor of rank three, making a compelling connection with tensor models. Furthermore, they have a natural interpretation in terms of D-brane constructions in string theory. I will present a way to define a large D scaling of the coupling constants such that the sum over Feynman graphs of fixed genus in matrix models admits a well-defined large D expansion. In particular, in the large D limit, the sum over planar graphs truncates to a tractable, yet non-trivial, sum over generalized melonic graphs. This family of graphs has been shown to display very interesting properties, especially in the case of quantum mechanical models such as the SYK model and SYK-like tensor models. If time allows, I will also explain how one can use the large D limit of matrix models to simplify the sum over all genera, which is notoriously divergent. 

According to the Asymptotic Safety conjecture, a (non-perturbatively)
renormalizable quantum field theory of gravity could be constructed
based on the existence of a non-trivial fixed point of the
renormalization group flow.
The existence of this fixed point can be established, e.g., via the
non-perturbative methods of the functional renormalization group (FRG).
In practice, the use of the FRG methods requires to work within
truncations of the gravitational action, and higher-derivative operators
naturally lead to the presence of several poles in the propagator. The
question is whether these poles represent a real problem for the
unitarity of the theory.

Using QED as a working example, in this talk I will discuss some aspects
of non-perturbative unitarity in Quantum Field Theory. I will show that
the inclusion of quantum effects at all scales is of crucial importance
to assess unitarity of field theories. In particular, poles appearing in
truncations of the action could correspond to fake degrees of freedom of
the theory. Possible conditions to determine, within truncations,
whether a pole represents a fake or a genuine degree of freedom of the
theory will also be discussed.

Hopf algebra lattice models are related to certain topological quantum field theories and give rise to topological invariants of oriented surfaces. Examples are the combinatorial quantisation of Chern-Simons theory and the Kitaev model.
Our main result is the construction of a mapping class group action on these models, formulated under weaker assumptions than the associated topological quantum field theories, namely for pivotal Hopf algebras in symmetric monoidal categories. This description also yields new structures for semisimple finite-dimensional Hopf algebras. The action of the mapping class group is defined in terms of simple graph transformations and allows one to compute quantum Dehn twists explicitly.

With the detection of GW170817 we have observed the first multi messenger signal from two merging neutron stars. This signal carried a multitude of information about the underlying equation of state (EOS) of nuclear matter, which so far is not known for densities above nuclear saturation. In particular it is not known if exotic states or even a phase transition to quark matter can occur at densities so extreme that they can't be probed by any current experiment.

I will show how the information carried in the gravitational wave signal of GW170817 can be used to constrain the EOS at densities above saturation and what we can learn about the possible existence of phase transitions. I will
also comment on how we can improve on those limits with upcoming observations of the NICER mission.In the second part of the talk I will focus on what we can learn about exotic states of matter from neutron star mergers.I will comment briefly on the impact of high spins in mergers and the importance of accurate numerical modelling in the context of these studies.Finally I will show how neutron star mergers can be used to study quark phase transitions and the phase diagram of QCD.