Symplectic SUSY Gauge Theories with Antisymmetric Matter

TL;DR

This paper derives exact superpotentials for specific confining supersymmetric $Sp(2N)$ gauge theories with fundamental and antisymmetric matter, revealing new insights into their vacuum structures and extending methods for analyzing such theories.

Contribution

It provides a systematic derivation of superpotentials for $Sp(4)$ and $Sp(6)$ theories with antisymmetric matter, which were previously undetermined by symmetry alone.

Findings

Exact superpotentials for $Sp(4)$ and $Sp(6)$ theories derived.

Analysis of ground state structures in product gauge group models.

Method demonstrated for finding superpotentials in other confining theories.

Abstract

We investigate the confining phase vacua of supersymmetric $Sp(2\NC)$ gauge theories that contain matter in both fundamental and antisymmetric representations. The moduli spaces of such models with $\NF=3$ quark flavors and $\NA=1$ antisymmetric field are analogous to that of SUSY QCD with $\NF=\NC+1$ flavors. In particular, the forms of their quantum superpotentials are fixed by classical constraints. When mass terms are coupled to $W_{(\NF=3,\NA=1)}$ and heavy fields are integrated out, complete towers of dynamically generated superpotentials for low energy theories with fewer numbers of matter fields can be derived. Following this approach, we deduce exact superpotentials in $Sp(4)$ and $Sp(6)$ theories which cannot be determined by symmetry considerations or integrating in techniques. Building upon these simple symplectic group results, we also examine the ground state structures of several $Sp(4) \times Sp(4)$ and $Sp(6) \times Sp(2)$ models. We emphasize that the top-down approach may be used to methodically find dynamical superpotentials in many other confining supersymmetric gauge theories.