Instanton corrections to the effective action of N=4 SYM

TL;DR

This paper calculates the one-instanton effective action for N=4 super Yang-Mills with gauge group Sp(2N), revealing non-perturbative corrections to higher derivative terms and confirming non-renormalization theorems.

Contribution

It provides a compact, supersymmetric form of the one-instanton effective action and verifies non-perturbative effects on higher derivative terms in N=4 SYM.

Findings

Instanton corrects higher derivative terms in Coulomb branch

Confirms non-renormalization theorems for MHV terms

Consistency with SL(2,Z) duality for F^4 term

Abstract

We compute the one-instanton effective action of N=4 super Yang-Mills theory with gauge group Sp(2N). The result can be written in a very compact and manifestly supersymmetric form involving an integral over the superspace of an irrational function of the N=4 on-shell superfields. In the Coulomb branch, the instanton corrects both the MHV and next-to-next-MHV higher derivative terms D^4F^{2n+2} and F^{2n+4}. We confirm at the non-perturbative level the non-renormalization theorems for MHV F^{2n+2} terms that are expected to receive perturbative corrections only at n-loops. We compute also the one and two-loop corrections to the D^4F^4 term and show that its completion under SL(2,Z) duality is consistent with the one-instanton results of U(2) gauge group.