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.
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.
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.
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).
I will discuss progress on a non-perturbative approach to the study of string sigma-models relevant in AdS/CFT which exploits lattice field theory techniques.
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
We construct the Haag Kaster net of von Neumann algebras for the Sine-Gordon model. This is joint work with Klaus Fredenhagen and Kasia Rejzner.