Symplectic SUSY gauge theories with antisymmetric matter.

Abstract

We investigate the confining phase vacua of supersymmetric $\mathrm{Sp}(2{N}_{C})$ gauge theories that contain matter in both fundamental and antisymmetric representations. The moduli spaces of such models with ${N}_{F}=3$ quark flavors and ${N}_{A}=1$ antisymmetric fields are analogous to that of SUSY QCD with ${N}_{F}={N}_{C}+1$ flavors. In particular, the forms of their quantum superpotentials are fixed by classical constraints. When mass terms are coupled to ${W}_{({N}_{F}=3,{N}_{A}=1)}$ 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)\ifmmode\times\else\texttimes\fi{}Sp(4) and Sp(6)\ifmmode\times\else\texttimes\fi{}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.