Relaxed super self-duality and N = 4 SYM at two loops

TL;DR

This paper derives a two-loop effective action for N=4 SYM on its Coulomb branch, revealing no F^4 or F^6 corrections at this order, thus supporting non-renormalization conjectures and challenging previous findings.

Contribution

It provides a closed-form expression for the two-loop effective action in N=4 SYM under relaxed super self-duality, highlighting the absence of certain quantum corrections.

Findings

No F^4 term at two loops, confirming non-renormalization conjectures.

No manifestly supersymmetric F^6 correction at two loops, contradicting previous results.

Effective action expressed in a holomorphic sector on Coulomb branch.

Abstract

A closed-form expression is obtained for a holomorphic sector of the two-loop low-energy effective action for the N = 4 super Yang-Mills theory on its Coulomb branch where the gauge group SU(N) is spontaneously broken to SU(N-1) x U(1) and the dynamics is described by a single Abelian N = 2 vector multiplet. In the framework of the background-field method, this holomorphic sector is singled out by computing the effective action for a background N = 2 vector multiplet satisfying a relaxed super self-duality condition. At the two-loop level, the N = 4 SYM effective action is shown to possess no F^4 term (with F the U(1) field strength), in accordance with the Dine-Seiberg non-renormalization conjecture hep-th/9705057 and its generalized form given in hep-th/0310025. An unexpected outcome of our calculation is that no (manifestly supersymmetric invariant generating) F^6 quantum correction occurs at two loops. This is in conflict with previous results.