Sum Rules from an Extra Dimension

TL;DR

This paper explores the analytic properties of thermal Green's functions in strongly coupled field theories via AdS/CFT, deriving sum rules and analyzing frequency behaviors using a new contraction mapping.

Contribution

It introduces a novel contraction mapping method to study Green's functions' large frequency behavior in the context of AdS/CFT correspondence.

Findings

Validated various sum rules for thermal Green's functions.

Analyzed large and small frequency behaviors of Green's functions.

Provided insights into pole structures of correlators.

Abstract

Using the gravity side of the AdS/CFT correspondence, we investigate the analytic properties of thermal retarded Green's functions for scalars, conserved currents, the stress tensor, and massless fermions. We provide some results concerning their large and small frequency behavior and their pole structure. From these results, it is straightforward to prove the validity of various sum rules on the field theory side of the duality. We introduce a novel contraction mapping we use to study the large frequency behavior of the Green's functions.