Some Systematics of the Coupling Constant Dependence of N=4 Yang-Mills

TL;DR

This paper investigates how the coupling constant influences correlation functions in N=4 Yang-Mills theory, revealing constraints and exact non-renormalization results for BPS operators through superconformal symmetry considerations.

Contribution

It demonstrates how superconformal Ward identities constrain the coupling dependence of correlation functions and establishes exact non-renormalization for specific BPS operator correlators.

Findings

Superconformal Ward identities determine terms in operator product expansions.

Constraints on coupling dependence of correlation functions are derived.

Exact non-renormalization of certain BPS operator correlators is proven.

Abstract

The operator, O_\tau, that generates infinitesimal changes of the coupling constant in N=4 Yang-Mills sits in the same supermultiplet as the superconformal currents. We show how superconformal current Ward identities determine a class of terms in the operator product expansion of O_\tau with any other operator. In certain cases, this leads to constraints on the coupling dependence of correlation functions in N=4 Yang-Mills. As an application, we demonstrate the exact non-renormalization of two and certain three-point correlation functions of BPS operators.