N=1 Deformations and RG Flows of N=2 SCFTs

TL;DR

This work analyzes a broad class of N=1 preserving deformations of four-dimensional N=2 SCFTs with non-Abelian flavor symmetry, implemented via a nilpotent Higgsing of an adjoint chiral M coupled to the moment map μ. Remarkably, many flows end at IR fixed points with enhanced N=2 supersymmetry, notably including generalized Argyres-Douglas theories such as (A1, A_{2N-1}) and (A1, A_{2N}), as well as various rank-one and class-S theories; in Lagrangian cases these flows permit exact computations of the full superconformal index and central charges. The authors develop a general anomaly/mixing framework based on a- and J_±-maximization to determine the IR R-symmetry and track decouplings of operators that hit unitarity bounds. They provide explicit Lagrangian descriptions for several non-Lagrangian AD theories, enabling detailed index computations that corroborate IR identifications and SUSY enhancement, and extend the analysis to T_N and R_{0,N} theories in class S. The results illuminate when principal (and other) nilpotent embeddings yield enhanced IR N=2 structure, and suggest criteria related to the Sugawara bound that may govern such enhancement.

Abstract

We study certain N=1 preserving deformations of four-dimensional N=2 superconformal field theories (SCFTs) with non-abelian flavor symmetry. The deformation is described by adding an N=1 chiral multiplet transforming in the adjoint representation of the flavor symmetry with a superpotential coupling, and giving a nilpotent vacuum expectation value to the chiral multiplet which breaks the flavor symmetry. This triggers a renormalization group flow to an infrared SCFT. Remarkably, we find classes of theories flow to enhanced N=2 supersymmetric fixed points in the infrared under the deformation. They include generalized Argyres-Douglas theories and rank-one SCFTs with non-abelian flavor symmetries. Most notably, we find renormalization group flows from the deformed conformal SQCDs to the $(A_1, A_n)$ Argyres-Douglas theories. From these "Lagrangian descriptions," we compute the full superconformal indices of the $(A_1, A_n)$ theories and find agreements with the previous results. Furthermore, we study the cases, including the $T_N$ and $R_{0,N}$ theories of class $\mathcal{S}$ and some of rank-one SCFTs, where the deformation gives genuine N=1 fixed points.