Week 02.10.2023 – 08.10.2023

We consider the renormalization group flow of a quantum field theory (QFT) in Anti-de Sitter (AdS) space. We derive sum rules that express UV data and the energy of a chosen eigenstate in terms of the spectral densities and certain correlation functions of the theory. In two dimensions, this leads to a bootstrap setup that involves the UV central charge and may allow us to follow a Renormalization Group (RG) flow non-perturbatively by continuously varying the AdS radius. Along the way, we establish the convergence properties of the newly discovered local block decomposition, which applies to three-point functions involving one bulk and two boundary operators.

The AdS3/CFT2 correspondence is the conjecture that gravity (more specifically superstrings) should be dual to some two-dimensional conformal field theory. Currently, the precise form of this CFT, or its features, are largely unknown. In this blackboard talk, I will review what is know, what is not, and how we are slowly but steadily making progress thanks to techniques from the world of integrable models.

We consider the renormalization group flow of a quantum field theory (QFT) in Anti-de Sitter (AdS) space. We derive sum rules that express UV data and the energy of a chosen eigenstate in terms of the spectral densities and certain correlation functions of the theory. In two dimensions, this leads to a bootstrap setup that involves the UV central charge and may allow us to follow a Renormalization Group (RG) flow non-perturbatively by continuously varying the AdS radius. Along the way, we establish the convergence properties of the newly discovered local block decomposition, which applies to three-point functions involving one bulk and two boundary operators.

In this talk, I will present a thorough investigation of the Wheeler-de Witt(WdW) equation within the framework of a Reissner-Nordstrom Anti-de Sitter (RN-AdS) black hole background and its relation to holographic renormalization flow. We solve the Wheeler DeWitt equation for the planar Reissner-Nordstrom-AdS black hole in a minisuperspace approximation and construct semiclassical Wheeler DeWitt states from Gaussian wavepackets that are peaked on classical black hole interior solutions. Furthermore, towards the AdS boundary, the Wheeler DeWitt states are used to recover the Lorentzian partition function of the dual theory living on this boundary. This partition function is specified by an energy and a charge. Finally, we show that the Wheeler DeWitt states know about the black hole thermodynamics, recovering the grand canonical thermodynamic potential after an appropriate averaging at the black hole horizon.

I will describe some recent developments in applying amplitude and effective field theory ideas in cosmology, and focus in particular on what cosmological measurements (of e.g. the cosmic microwave background or large-scale structure of galaxies) can tell us about the underlying fundamental field theory.