Emmy Noether Workshop: The Structure of Quantum Space Time

Cosmologists wish to explain how our universe, in all its complexity, could ever have come about. For that, we assess the number degrees of freedom in our Universe now. This plays the role of entropy in thermodynamics of the Universe, and reveals the magnitude of the problem of initial conditions to be solved. In our budget, we account for gravity, thermal motions, and finally the vacuum energy whose entropy, given by the Bekenstein bound, dominates the entropy budget today. There is however one number which we have not accounted for: the number of degrees of freedom in our complex biosphere. What is the entropy of life? Is it sizeable enough to need to be accounted for at the Big Bang, or negligible compared to vacuum entropy?

Recent developments on asymptotic symmetries and soft modes have deepened our understanding of black hole entropy and the information paradox. The asymptotic symmetry charge algebra of certain classes of spacetimes could have a nontrivial central extension, which plays a crucial role in black hole physics. The Cardy formula of the asymptotic density of states of the dual CFT has been famously used to reproduce the Bekenstein-Hawking entropy formula. However, without assuming holography, it remains obscure from the point of view of gravity how such a constant on the gravitational phase space encodes the information about the density of black hole microstates, and what the gravitational degrees of freedom accounting for the black hole entropy truly are. I will discuss my ongoing efforts of understanding these questions in the covariant phase space formalism.

Higher spin symmetries are gauge symmetries sourced by massless particles with spin greater than two. When coupled with diffeomorphism, they give rise to higher spin gravity. After a review on higher spin gravity, I will discuss its holography and its embedding in the string theory. Finally I will talk about some applications of higher spin symmetry, both in string theory and in QFT.

A spectral triple consists of an algebra, a Hilbert space and a Dirac operator, and if these three fulfill certain relations to each other they contain the entire information of a compact Riemannian manifold. Using the language of spectral triples makes it possible to generalize the concept of a manifold to include non-commutativity. While it is possible to write down finite spectral triples, often categorized as fuzzy spaces, that describe discretized geometries, classical geometries are encoded in infinite dimensional spectral triples. However working in numerical systems (and maybe ultimately in physical systems), only a finite part of this information can be encoded, which opens the question; If we know a part of the spectrum, how clearly can we characterise a geometry. In this talk I will present first steps towards answering this question.

I describe a radical proposal for the cosmological constant problem: perhaps Lambda really is very large, but is "hidden" in Planck-scale fluctuations of geometry and topology. I show that an enormous set of initial data describe a universe with such a hidden cosmological constant at an initial time. The question of whether this structure is preserved under time evolution is still open, but I provide some evidence that it may be. I close with a discussion of open questions that might lead to further insight (or perhaps kill the idea).

During this talk we shall discuss the backreaction of quantum matter fields on classical backgrounds by means of the semiclassical Einstein equation. We shall see that self consistent solutions of this coupled system exist in the case of cosmological spacetimes. Furthermore, Einstein equations governing the backreaction will transfer quantum matter fluctuations to the metric. In particular, we will see how the singular structure of quantum matter will affect the spectrum of metric perturbations

I will discuss the application of Siegel paramodular forms to constructing new examples of holography. These forms are relevant to investigate the growth of coefficients in the elliptic genus of symmetric product orbifolds at large central charge. The main finding is that the landscape of symmetric product theories decomposes into two regions. In one region, the growth of the low energy states is Hagedorn, which indicates a stringy dual. In the other, the growth is much slower, and compatible with the spectrum of a supergravity theory on AdS_3. I will provide a simple diagnostic which places any symmetric product orbifold in either region. The examples I will present open a path to novel realizations of AdS_3/CFT_2.

I'll describe my recent work on black hole seeded vacuum decay, and proposals for testing seeded decay in cold atom experiments. I'll conclude with speculations on seeking insight into quantum black holes via experimentally constructing quantised analog black holes.