Symplectic SUSY Gauge Theories with Antisymmetric Matter

TL;DR

The work studies confining vacua of $Sp(2N_C)$ gauge theories with fundamental and antisymmetric matter, showing that for $N_F=3$, $N_A=1$ the moduli space and the form of the quantum superpotential are fixed by classical constraints, mirroring the SUSY QCD result $W_{N_F=N_C+1}=({\bar B M B - \det M})/\Lambda^{2N_C-1}$. A top-down approach, using mass deformations and integrating out heavy fields, yields a tower of dynamical superpotentials and exact results for $Sp(4)$ and $Sp(6)$, including cases unreachable by symmetry or integrating in. These results extend to product groups such as $Sp(4)\times Sp(4)$ and $Sp(6)\times Sp(2)$ by assembling sector contributions with threshold matching and parity considerations, producing comprehensive infrared superpotentials. Overall, the paper demonstrates a general method to derive nonperturbative dynamics in confining supersymmetric theories from classical data, with broad applicability to other gauge groups and matter content.

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.