An elliptic superpotential for softly broken N = 4 supersymmetric Yang-Mills theory

Abstract

An exact superpotential is derived for the N = 1 theories which arise as massive deformations of N = 4 supersymmetric Yang-Mills (SYM) theory. The superpotential of the SU(N) theory formulated on ℝ3 × S1 is shown to coincide with the complexified potential of the N-body elliptic Calogero-Moser hamiltonian. This superpotential reproduces the vacuum structure predicted by Donagi and Witten for the corresponding four-dimensional theory and also transforms covariantly under the S-duality group of N = 4 SYM. The analysis yields exact formulae with interesting modular properties for the condensates of gauge-invariant chiral operators in the four-dimensional theory.