Supersymmetric Adler Functions and Holography

TL;DR

This paper tests a proposed exact formula for current correlation functions in supersymmetric gauge theories, confirming its validity in superconformal cases and identifying its limitations in theories with mass terms.

Contribution

It clarifies the meaning of the formula in superconformal theories and demonstrates its automatic consistency with known relations and dualities, while showing where it fails.

Findings

The formula matches known relations in superconformal theories.

It automatically aligns with dual descriptions of the same theory.

The formula fails in theories with mass terms, as shown by holographic and free theory examples.

Abstract

We perform several tests on a recent proposal by Shifman and Stepanyantz for an exact expression for the current correlation functions in supersymmetric gauge theories. We clarify the meaning of the relation in superconformal theories. In particular we show that it automatically follows from known relations between the current correlation functions and anomalies. It therefore also automatically matches between different dual realizations of the same superconformal theory. We use holographic examples as well as calculations in free theories to show that the proposed relation fails in theories with mass terms.