Exact Results and Duality for SP(2N) SUSY Gauge Theories with an Antisymmetric Tensor

TL;DR

This work analyzes $Sp(2N)$ gauge theories with an antisymmetric tensor and $F$ fundamentals, uncovering rich non-perturbative dynamics across flavor number $F$. For $F=6$ the theory confines without chiral-symmetry breaking and is exactly described by IR invariants $T_k$ and $M_k$ through a confining superpotential; mass deformations yield quantum-deformed moduli spaces and instanton-generated superpotentials for lower $F$, including a two-branch structure at $F=0$. A Seiberg-like dual for $F=8$ is constructed with the same gauge group but augmented by mesons and a specific superpotential, and anomaly matching plus flows to $F=6$ validate the dual. The paper also demonstrates concrete model-building applications, such as dynamical SUSY breaking and composite-model scenarios in which confinement of $Sp(6)$ produces SM-like generations and hierarchical Yukawas. Overall, these results extend exact non-perturbative insights to $Sp(2N)$ theories with tensor matter and provide new templates for beyond-Standard-Model physics.

Abstract

We study supersymmetric Sp(2N) gauge theories with matter in the antisymmetric tensor representation and F fundamentals. For F=6 we solve the theory exactly in terms of confined degrees of freedom and a superpotential. By adding mass terms we obtain the theories with F<6 which we find to exhibit a host of interesting non-perturbative phenomena: quantum deformed moduli spaces with N constraints, instanton-induced superpotentials and non-equivalent disjoint branches of moduli spaces. We find a simple dual for F=8 and no superpotential. We show how the F=4 and F=2 theories can be modified to break supersymmetry spontaneously and point out that the Sp(6) theory with F=6 may be very interesting for model builders.