On instanton effects in the operator product expansion

TL;DR

This paper investigates instanton effects in ${\cal N}=4$ SYM, confirming their consistency with conformal symmetry and the operator product expansion, and clarifying previous controversies through detailed conformal partial wave analysis.

Contribution

It provides a detailed analysis of instanton contributions to correlation functions, validating regularization methods and clarifying their role in conformal symmetry and OPE consistency.

Findings

Instanton corrections are consistent with conformal symmetry.

Computed corrections to OPE coefficients and scaling dimensions.

Validated regularization procedures for divergent instanton contributions.

Abstract

We revisit the computation of instanton effects to various correlation functions in ${\cal N}=4$ SYM and clarify a controversy existing in the literature regarding their consistency with the OPE and conformal symmetry. To check these properties, we examine the conformal partial wave decomposition of four-point correlators involving combinations of half-BPS and Konishi operators and isolate the contribution from the conformal primary scalar operators of twist four. We demonstrate that the leading instanton correction to this contribution is indeed consistent with conformal symmetry and compute the corresponding corrections to the OPE coefficients and the scaling dimensions of such twist-four operators. Our analysis justifies the regularization procedure used to compute ultraviolet divergent instanton contribution to correlation functions involving unprotected operators.