Week 13.11.2023 – 19.11.2023

In these series of lectures we will explore initial value problem in general relativity and how it can be solved in a computer in practical situations. We will first cover the necessary mathematical foundations, including the concepts of well-posedness and strong hyperbolicity, and then explore the current formulations of Einstein’s theory of gravity that are implemented in modern numerical codes, namely generalised harmonic coordinates and the BSSN formulation. We shall see how the latter can be implemented in a toy code so as to get some hands on experience. Time permitting, we will also explore the initial boundary value problem in asymptotically anti-de Sitter spaces and how it can be solved in practice using the characteristic formulation of the Einstein equations in applications of holography.

Long range entanglement is a conceptually useful notion in the physics of quantum phases of matter. E.g. in (2+1) dimensions, ground states display area law entanglement with a potential constant correction: the "topological entanglement entropy" (TEE) which is a smoking gun of topological order. Through the lens of the IR effective field theory, described by topological quantum field theory (TQFT), we encounter the following puzzle: how does a field theory with a finite dimensional Hilbert space support a divergent area law? The simple resolution to this puzzle will also suggest an alternative perspective on topological entanglement. Utilizing the algebraic formulation of entanglement I will define a quantity I will call "essential topological entanglement." It is (i) strictly topological, (ii) positive, (iii) finite, and (iv) displays more long-range features than traditional TEE. Working with Abelian p-form BF theory as an example, I will explain general aspects of essential topological entanglement. I will elaborate on potential further applications of essential topological entanglement, as well as describe some follow-up work regarding the entanglement carried by edge-modes in BF theory.

Decoherence and thermalisation of isolated many-particle quantum states are studied in many different subfields of physics, including high-energy physics. One of the most interesting case are Heavy Ion Collisions which can be holographically connected to string theory in Anti-de Sitter space and for which very detailed data exists. After a general introduction I will focus on the question whether SU(N) gauge theories behave as predicted by the Eigenstate Thermalization Hypothesis (ETH). To answer this question we have performed simulations for low-dimensional SU(2) gauge theories on digital computers (arXiv: 2308.16202) which gave encouraging results. As ETH makes predictions for energy eigenstates the most natural theoretical approach to study e.g. thermalization of QCD is the numnerical simulation of Hamiltonian lattice QCD on quantum computers which, however, is not yet possible. Investigating the validity of ETH on digital computers is an early step in this direction.

In this talk I will provide briefly summarize the status of numerical lattice simulations of supersymmetric gauge theories. As an example I will focus on low dimensional supersymmetric Yang-Mills theories in the context of gauge/gravity duality.

I this talk I will describe a picture which has emerged over the past few years regarding the statistical interpretation of semiclassical gravity and how this relates to wormholes, averaging and the so-called factorization puzzle, the information paradox, and a combinatorial description of 3d gravity.

I will describe a novel class of statistical ensembles we developed for the description of chaotic conformal field theories. These are generalisations of the usual random-matrix type theories used in the description of quantum chaotic many-body systems, and implement the kinematical as well as dynamical constraints of the CFT bootstrap. These novel statistical models take the form of distributions over random matrices and tensors. I will take some time to characterise the individual elements in terms of so-called “approximate CFTs”. Finally, I will discuss the concrete realisation of these ideas for 2D, large-c CFT and point out that the resulting tensor models (subject to reasonable constraints on the spectrum) take the form of an integral over random discrete triangularisation of 3D Euclidean manifolds, governed by the 6j symbols of Virasoro, strongly suggesting a connection to three dimensional quantum gravity.

A day for gravity