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

TL;DR

This paper investigates N=1 preserving deformations of N=2 SCFTs, revealing RG flows to both N=2 and N=1 fixed points, including Argyres-Douglas theories, and computes superconformal indices for these flows.

Contribution

It introduces a class of deformations leading to new RG flows, including flows from conformal SQCDs to Argyres-Douglas theories, with explicit index computations and analysis of fixed points.

Findings

RG flows from deformed SQCDs to (A1, An) Argyres-Douglas theories

Superconformal indices match previous results for (A1, An) theories

Identification of genuine N=1 fixed points in certain deformations

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.