Enhancement of Supersymmetry via Renormalization Group Flow and the Superconformal Index

TL;DR

The paper constructs an N=1 gauge theory via a principal nilpotent deformation of N=2 SU(2) with Nf=4, which flows to the minimal Argyres-Douglas N=2 SCFT plus four free chiral multiplets. Through a-maximization and careful decoupling of unitarity-violating operators, the IR fixed point is shown to match the AD theory with central charges a=43/120 and c=11/30, and a Coulomb-branch operator of dimension Δ=6/5. The authors then compute the full superconformal index for the UV theory, map it to the N=2 index, and verify consistency with AD results across Coulomb, Macdonald, and Schur limits (including the Yang-Lee chiral algebra). This work provides a Lagrangian handle on a non-Lagrangian SCFT and demonstrates a robust framework for exploring its protected spectrum and partition functions, with potential generalizations to other AD theories.

Abstract

We find a four-dimensional N=1 gauge theory which flows to the minimal interacting N=2 superconformal field theory, the Argyres-Douglas theory, in the infrared up to the extra free chiral multiplets. The gauge theory is obtained from a certain N=1 preserving deformation of the N=2 SU(2) gauge theory with four fundamental hypermultiplets. From this description, we compute the full superconformal index and find agreements with the known results in special limits.