Relaxed super self-duality and N = 4 SYM at two loops
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.
Keywords
Cite
@article{arxiv.hep-th/0403240,
title = {Relaxed super self-duality and N = 4 SYM at two loops},
author = {S. M. Kuzenko and I. N. McArthur},
journal= {arXiv preprint arXiv:hep-th/0403240},
year = {2009}
}
Comments
43 pages, latex, 1 eps figure; V2: appendix, comments, references added (46 pages); V3: comments, references added (47 pages), to appear in NPB