N=1 Deformations and RG Flows of N=2 SCFTs, Part II: Non-principal deformations

TL;DR

This paper studies specific deformations of four-dimensional N=2 superconformal field theories that trigger RG flows to N=1 SCFTs, revealing supersymmetry enhancement and dualities, and enabling superconformal index computations for certain Argyres-Douglas theories.

Contribution

It systematically analyzes non-principal N=1 deformations of N=2 SCFTs, discovering supersymmetry enhancement and dualities, and connecting RG flows to superconformal index calculations.

Findings

Deformations of SQCDs flow to Argyres-Douglas theories.

Supersymmetry enhancement occurs at RG flow endpoints.

Infrared dualities relate N=1 theories to N=2 AD fixed points.

Abstract

We continue to investigate the $\mathcal{N}=1$ deformations of four-dimensional $\mathcal{N}=2$ superconformal field theories (SCFTs) labeled by a nilpotent element of the flavor symmetry. This triggers a renormalization group (RG) flow to an $\mathcal{N}=1$ SCFT. We systematically analyze all possible deformations of this type for certain classes of $\mathcal{N}=2$ SCFTs: conformal SQCDs, generalized Argyres-Douglas theories and the $E_6$ SCFT. We find a number of examples where the amount of supersymmetry gets enhanced to $\mathcal{N}=2$ at the end point of the RG flow. Most notably, we find that the $SU(N)$ and $Sp(N)$ conformal SQCDs can be deformed to flow to the Argyres-Douglas (AD) theories of type $(A_1, D_{2N-1})$ and $(A_1, D_{2N})$ respectively. This RG flow therefore allows us to compute the full superconformal index of the $(A_1,D_N)$ class of AD theories. Moreover, we find an infrared duality between $\mathcal{N}=1$ theories where the fixed point is described by an $\mathcal{N}=2$ AD theory. We observe that the classes of examples that exhibit supersymmetry enhancement saturate certain bounds for the central charges implied by the associated two-dimensional chiral algebra.