Bulk spectral function sum rule in QCD-like theories with a holographic dual

TL;DR

This paper derives a sum rule for the spectral function of the stress-energy tensor in a broad class of strongly coupled theories with holographic duals, connecting it to QCD and verifying it through a holographic model.

Contribution

It establishes a general sum rule in holographic theories with a scalar field, including QCD-like theories, and verifies it explicitly using a holographic model.

Findings

Sum rule derived for spectral function in holographic theories.

Verification of sum rule through explicit holographic model calculations.

Connection established between holographic models and QCD in the marginal operator limit.

Abstract

We derive the sum rule for the spectral function of the stress-energy tensor in the bulk (uniform dilatation) channel in a general class of strongly coupled field theories. This class includes theories holographically dual to a theory of gravity coupled to a single scalar field, representing the operator of the scale anomaly. In the limit when the operator becomes marginal, the sum rule coincides with that in QCD. Using the holographic model, we verify explicitly the cancellation between large and small frequency contributions to the spectral integral required to satisfy the sum rule in such QCD-like theories.