Matrix-model description of [formula omitted] gauge theories with non-hyperelliptic Seiberg–Witten curves

Abstract

Using matrix-model methods we study three different N=2 models: U( N)× U( N) with matter in the bifundamental representation, U( N) with matter in the symmetric representation, and U( N) with matter in the antisymmetric representation. We find that the (singular) cubic Seiberg–Witten curves (and associated Seiberg–Witten differentials) implied by the matrix models, although of a different form from the ones previously proposed using M-theory, can be transformed into the latter and are thus physically equivalent. We also calculate the one-instanton corrections to the gauge-coupling matrix using the perturbative expansion of the matrix model. For the U( N) theories with symmetric or antisymmetric matter we use the modified matrix-model prescription for the gauge-coupling matrix discussed in our paper: Cubic curves from matrix models and generalized Konishi anomalies ( hep-th/0303268). Moreover, in the matrix model for the U( N) theory with antisymmetric matter, one is required to expand around a different vacuum than one would naively have anticipated. With these modifications of the matrix-model prescription, the results of this paper are in complete agreement with those of Seiberg–Witten theory obtained using M-theory methods.