Duality in Supersymmetric SU($N_c$) Gauge Theory with Two Adjoint Chiral Superfields

TL;DR

This paper explores a duality in supersymmetric SU(N_c) gauge theories with two adjoint superfields and fundamental matter, introducing a new dual description and analyzing its flow to a product gauge group duality.

Contribution

It presents a novel duality for SU(N_c) gauge theories with two adjoint superfields and a specific superpotential, including a flow to a product gauge group duality.

Findings

Duality passes multiple consistency tests.

Deformation leads to a product gauge group duality.

Explicit dual descriptions for complex superpotentials.

Abstract

We discuss $SU(N_c)$ gauge theory coupled to two adjoint chiral superfields $X$ and $Y$, and a number of fundamental chiral superfields $Q^i$. We add a superpotential that has the form of Arnold's $D$ series $W = \Tr X^{k+1} + \Tr XY^2$. We present a dual description in terms of an $SU(3kN_f - N_c)$ gauge theory, and we show that the duality passes many tests. At the end of the paper, we show how a deformation of this superpotential flows to another duality having a product gauge group $SU(N_c)\times SU(N_c')$, with an adjoint field charged under $SU(N_c)$, an adjoint field charged under $SU(N_c')$, fields in the $(N_c,N_c')$ and $(\overline N_c,\overline N_c')$ representation, and a number of fundamentals. The dual description is an $SU(2kN_f' + kN_f - N_c')\times SU(2kN_f + kN_f' - N_c)$ gauge theory.