Bulk spectral functions in single and multi-scalar gravity duals

TL;DR

This paper develops a generalized method to compute bulk spectral functions in gravity dual theories with multiple scalar fields, and applies it to analyze sum rules in specific backgrounds related to gauge theories.

Contribution

It introduces a new prescription for bulk spectral functions in multi-scalar gravity duals, extending previous single-scalar approaches.

Findings

Derived a generalized prescription for bulk spectral functions.

Applied the method to the Chamblin-Reall background.

Connected the sum rule to the beta function, similar to Yang-Mills theory.

Abstract

We examine two point correlation functions involving the trace of the energy momentum tensor in five dimensional gravity dual theories supported by one or more scalar fields. A prescription for determining bulk channel spectral functions is developed. This prescription generalizes previous work which centered on one scalar field. As an application of these techniques, we investigate the bulk spectral function and corresponding sum rule in the Chamblin-Reall background. We show that, when expressed in terms of the beta function, the sum rule for the Chamblin-Reall background can be written in a form similar to the sum rule in Yang-Mills theory.