A shear spectral sum rule in a non-conformal gravity dual

TL;DR

This paper investigates a sum rule relating stress-energy tensor correlators to thermodynamics in a non-conformal gravity dual, revealing it does not generalize from conformal theories and providing a new generalized sum rule.

Contribution

The paper derives a generalized sum rule for non-conformal theories and verifies it numerically, extending previous conformal results to a broader class of theories.

Findings

The original sum rule does not hold in the non-conformal case.

A new generalized sum rule is proposed and numerically confirmed.

Spectral densities in a strongly coupled non-conformal theory are computed.

Abstract

A sum rule which relates a stress-energy tensor correlator to thermodynamic functions is examined within the context of a simple non-conformal gravity dual. Such a sum rule was previously derived using AdS/CFT for conformal $\mathcal{N} = 4$ Supersymmetric Yang-Mills theory, but we show that it does not generalize to the non-conformal theory under consideration. We provide a generalized sum rule and numerically verify its validity. A useful byproduct of the calculation is the computation of the spectral density in a strongly coupled non-conformal theory. Qualitative features of the spectral densities and implications for lattice measurements of transport coefficients are discussed.