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arXiv · hep-th/0403240

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

S. M. Kuzenko·I. N. McArthur
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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.

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S. M. Kuzenko, I. N. McArthur. 2004-07-22. Relaxed super self-duality and N = 4 SYM at two loops. https://doi.org/10.1016/j.nuclphysb.2004.07.026

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