Revisiting instanton corrections to the Konishi multiplet

TL;DR

This paper investigates instanton effects in ${ m N}=4$ SYM, revealing how quantum corrections can be computed across supermultiplet members, leading to explicit instanton corrections for Konishi operators and twist-four operators with large spin.

Contribution

It introduces a method to relate quantum instanton corrections of different supermultiplet operators, enabling explicit calculations beyond the semiclassical approximation.

Findings

Explicit instanton correction to Konishi operator's scaling dimension

Instanton corrections to OPE structure constants of half-BPS operators

Determination of instanton effects on large spin twist-four operators

Abstract

We revisit the calculation of instanton effects in correlation functions in ${\cal N}=4$ SYM involving the Konishi operator and operators of twist two. Previous studies revealed that the scaling dimensions and the OPE coefficients of these operators do not receive instanton corrections in the semiclassical approximation. We go beyond this approximation and demonstrate that, while operators belonging to the same ${\cal N}=4$ supermultiplet ought to have the same conformal data, the evaluation of quantum instanton corrections for one operator can be mapped into a semiclassical computation for another operator in the same supermultiplet. This observation allows us to compute explicitly the leading instanton correction to the scaling dimension of operators in the Konishi supermultiplet as well as to their structure constants in the OPE of two half-BPS scalar operators. We then use these results, together with crossing symmetry, to determine instanton corrections to scaling dimensions of twist-four operators with large spin.