Matrix-model description of N=2 gauge theories with non-hyperelliptic Seiberg-Witten curves

TL;DR

This paper employs matrix-model techniques to analyze N=2 gauge theories with non-hyperelliptic Seiberg-Witten curves, demonstrating their equivalence to M-theory results and computing instanton corrections.

Contribution

It introduces a matrix-model approach to non-hyperelliptic Seiberg-Witten curves, showing their physical equivalence to M-theory formulations and calculating instanton effects.

Findings

Seiberg-Witten curves can be transformed into M-theory forms.

One-instanton corrections to gauge couplings are computed.

Modified matrix-model prescriptions are necessary for certain matter representations.

Abstract

Using matrix-model methods we study three different N=2 models: U(N) x 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 ref. [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.