Higgsing and Superpotential Deformations of ADE Superconformal Theories

TL;DR

This paper investigates the renormalization group flows in 4d supersymmetric gauge theories with ADE-type superpotentials, analyzing how Higgsing and superpotential deformations affect their conformal fixed points and R-charges.

Contribution

It applies $a$-maximization to study RG flows and conformal fixed points in ADE theories, including Higgsing effects and magnetic dual descriptions, providing new insights into their dynamics.

Findings

Computed R charges and checked the $a$-theorem for various flows.

Identified parameter regions where Higgsed theories remain conformal.

Used magnetic duals to analyze non-trivial fixed points.

Abstract

We study large classes of renormalization group flows, driven by scalar expectation values or mesonic superpotential terms, away from the conformal fixed points of the 4d supersymmetric gauge theories with $ADE$-type superpotentials. The $a$-maximization procedure allows us to compute the $R$ charges and to check the $a$-theorem conjecture. For a theory obtained by Higgsing the $D_{k+2}$ theory, we use the magnetic dual description proposed by Brodie to determine the parameter region where the resulting theory is at a non-trivial conformal fixed point.