Notes on supersymmetric Sp(N) theories with an antisymmetric tensor

TL;DR

This paper analyzes supersymmetric Sp(N) gauge theories with an antisymmetric tensor, using anomaly equations to compute the low energy superpotential and establishing a precise mapping to U(N+2n) theories.

Contribution

It introduces a method to compute the superpotential in Sp(N) theories with an antisymmetric tensor using anomaly equations and maps these theories to U(N+2n) models.

Findings

Explicit superpotential computations for Sp(2), Sp(4), Sp(6), Sp(8)

Agreement with dynamical superpotential results

Map from Sp(N) to U(N+2n) theories

Abstract

We study supersymmetric Sp(N) gauge theories with an antisymmetric tensor and degree n+1 tree level superpotential. The generalized Konishi anomaly equations derived in hep-th/0304119 and hep-th/0304138 are used to compute the low energy superpotential of the theory. This is done by imposing a certain integrality condition on the periods of a meromorphic one form. Explicit computations for Sp(2), Sp(4), Sp(6) and Sp(8) with cubic superpotential are done and full agreement with the results of the dynamically generated superpotential approach is found. As a byproduct, we find a very precise map from Sp(N) to a U(N+2n) theory with one adjoint and a degree n+1 tree level superpotential.