# On the Chiral Ring and Vacua of ${\cal N}=1$ Adjoint SQCD

## TL;DR

This paper investigates the classical and quantum chiral ring relations in ${
m extbf{N}=1}$ adjoint SQCD with superpotential deformations, revealing detailed vacuum structures and the correspondence between chiral ring solutions and supersymmetric vacua.

## Contribution

It provides a comprehensive analysis of the vacuum structure and chiral ring relations in ${
m extbf{N}=1}$ adjoint SQCD, including the effects of mass deformations and quantum corrections.

## Key findings

- Complete vacuum expectation values for gauge invariant operators in mass-deformed theory
- Identification of non-trivial flat directions and quantum-corrected Higgs branches
- Establishment of a one-to-one correspondence between chiral ring solutions and supersymmetric vacua

## Abstract

We analyze classical and quantum chiral ring relations of four dimensional ${\cal N} = 1$ adjoint SQCD with superpotential turned on for the adjoint field. In particular, for the mass deformed theory we obtain the complete on shell vacuum expectation value for various gauge invariant chiral operators and find non-trivial gaugino condensations. When approaching to massless limit nontrivial flat directions in the moduli space of vacua appear, where the Coulomb branch can be naturally classified and the Higgs branch receives quantum corrections. We argue that the solution of the chiral ring is in one-to-one correspondence with supersymmetric vacua, provided that an additional Konishi anomaly equation is included.