M theory and the ``integrating in'' method with an antisymmetric tensor

TL;DR

This paper explores the Coulomb branch of N=2 SUSY SU(N_c) Yang-Mills theory with an antisymmetric tensor, using M theory five-brane configurations and the 'integrating in' method, revealing the need for an additional superpotential for consistency.

Contribution

It introduces a non-hyperelliptic curve description of the Coulomb branch and identifies an essential additional superpotential term for consistency with field theory results.

Findings

Explicit form of the superpotential W_Δ is derived.

Comparison between M theory curve and field theory results is established.

Additional superpotential is necessary for consistency.

Abstract

Recently, a non-hyperelliptic curve describing the Coulomb branch of N=2 SUSY $SU(N_c)$ Yang-Mills theory with an antisymmetric tensor matter was proposed using a configuration of a single M theory five-brane. We study the singular surface in the moduli space of the curve to compare it with results from the ``integrating in'' method in field theory. In order to achieve the consistency, we find it necessary to take account of an additional superpotential $W_{\Delta}$ which has been neglected so far. The explicit form of $W_{\Delta}$ is worked out.