Low-Energy Theorems from Holography

TL;DR

This paper verifies low-energy theorems in gauge theories using holography, providing analytic proofs and numerical evidence for dilation Ward identities and decoupling theorems across different models, and explores their implications for meson transport.

Contribution

It offers the first analytic proof of dilation Ward identities in holography and demonstrates the universal validity of decoupling theorems across multiple models, extending low-energy theorem understanding.

Findings

Analytic proof of dilation Ward identities in holographic models.

Numerical confirmation of decoupling theorem in three different backgrounds.

Gauge field condensate contributions to meson transport coefficients.

Abstract

In the context of gauge/gravity duality, we verify two types of gauge theory low-energy theorems, the dilation Ward identities and the decoupling of heavy flavor. First, we provide an analytic proof of non-trivial dilation Ward identities for a theory holographically dual to a background with gluon condensate (the self-dual Liu--Tseytlin background). In this way an important class of low-energy theorems for correlators of different operators with the trace of the energy-momentum tensor is established, which so far has been studied in field theory only. Another low-energy relationship, the so-called decoupling theorem, is numerically shown to hold universally in three holographic models involving both the quark and the gluon condensate. We show this by comparing the ratio of the quark and gluon condensates in three different examples of gravity backgrounds with non-trivial dilaton flow. As a by-product of our study, we also obtain gauge field condensate contributions to meson transport coefficients.