Renormalization group flows in AdS and the bootstrap program

TL;DR

This paper develops a bootstrap framework in AdS space to analyze RG flows of quantum field theories by deriving sum rules from stress tensor correlators, enabling non-perturbative RG tracking.

Contribution

It introduces a new bootstrap setup in AdS2 involving the central charge and establishes convergence of a local block decomposition for three-point functions.

Findings

Derived new sum rules from stress tensor correlators.

Established convergence of local block decomposition.

Proposed a non-perturbative RG flow analysis in AdS2.

Abstract

We study correlation functions of the bulk stress tensor and boundary operators in Quantum Field Theories (QFT) in Anti-de Sitter (AdS) space. In particular, we derive new sum rules from the two-point function of the stress tensor and its three-point function with two boundary operators. In AdS2, this leads to a bootstrap setup that involves the central charge of the UV limit of the bulk QFT 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 of the three-point function.