Effective superpotential for U(N) with antisymmetric matter

TL;DR

This paper derives the effective superpotential for a U(N) gauge theory with antisymmetric matter, revealing non-trivial N-dependence and connections to Sp(2N-2) theories, advancing understanding of supersymmetric gauge dynamics.

Contribution

It provides an explicit calculation of the effective superpotential for U(N) with antisymmetric matter, including N-dependence and contributions from Sp(0) factors, and maps to Sp(2N-2) theories.

Findings

Effective superpotential with non-factorizing N-dependence.

Identification of contributions from Sp(0) factors at order S^N.

Mapping of U(N) antisymmetric theory to Sp(2N-2) gauge theory.

Abstract

We consider an N=1 U(N) gauge theory with matter in the antisymmetric representation and its conjugate, with a tree level superpotential containing at least quartic interactions for these fields. We obtain the effective glueball superpotential in the classically unbroken case, and show that it has a non-trivial N-dependence which does not factorize. We also recover additional contributions starting at order S^N from the dynamics of Sp(0) factors. This can also be understood by a precise map of this theory to an Sp(2N-2) gauge theory with antisymmetric matter.