# Instanton effects in correlation functions on the light-cone

## TL;DR

This paper investigates instanton effects on four-point correlation functions of half-BPS operators in N=4 SYM in the light-cone limit, linking them to Wilson loops and computing instanton contributions to anomalous dimensions.

## Contribution

It provides the first semiclassical calculation of instanton corrections to light-like Wilson loops and related anomalous dimensions in N=4 SYM, verifying conformal Ward identities nonperturbatively.

## Key findings

- Instanton corrections to four-point functions are computed via Wilson loops.
- Light-like rectangular Wilson loops satisfy anomalous conformal Ward identities with instantons.
- Leading instanton contributions to cusp and twist-two anomalous dimensions are obtained.

## Abstract

We study instanton corrections to four-point correlation correlation function of half-BPS operators in $\mathcal N=4$ SYM in the light-cone limit when operators become null separated in a sequential manner. We exploit the relation between the correlation function in this limit and light-like rectangular Wilson loop to determine the leading instanton contribution to the former from the semiclassical result for the latter. We verify that the light-like rectangular Wilson loop satisfies anomalous conformal Ward identities nonperturbatively, in the presence of instantons. We then use these identities to compute the leading instanton contribution to the light-like cusp anomalous dimension and to anomalous dimension of twist-two operators with large spin.