# The Phase Structure of Supersymmetric Sp(2N_c) Gauge Theories with an Adjoint

## TL;DR

This paper analyzes the phase structure of N=1 supersymmetric Sp(2N_c) gauge theories with an adjoint and fundamentals, using a-maximization to identify when operators become free and comparing dual descriptions for consistency.

## Contribution

It provides explicit analytic expressions for the unitarity bound violations and confirms previous conjectures through duality analysis without evidence of accidental symmetries.

## Key findings

- Operators become free below certain N_f values
- Dual descriptions agree with the original theory
- No evidence of accidental symmetries or mixed phases

## Abstract

We study the phase structure of N = 1 supersymmetric Sp(2N_c) gauge theories with 2N_f fundamentals, an adjoint, and vanishing superpotential. Using a-maximization, we derive analytic expressions for the values of N_f below which the first several gauge-invariant operators in the chiral ring violate the unitarity bound and become free fields. In doing so we are able to explicitly check previous conjectures about the behavior of this theory made by Luty, Schmaltz, and Terning. We then compare this to an analysis of the first two 'deconfined' dual descriptions based on the gauge groups Sp(2N_f+2) x SO(2N_c+5) and Sp(2N_f+2) x SO(4N_f+4) x Sp(2N_c+2), finding precise agreement. In particular, we find no evidence for non-obvious accidental symmetries or the appearance of a mixed phase in which one of the dual gauge groups becomes free.