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

TL;DR

The work develops and systematizes ${ m N}=1$ deformations of four-dimensional ${ m N}=2$ SCFTs via nilpotent vevs of a flavor-adjoint field, revealing a rich web of IR fixed points. A-maximization with operator decoupling is used to determine IR R-symmetries and central charges, uncovering multiple flows to Argyres-Douglas theories, including ${ m (A_1,D_{2N})}$ and ${ m (A_1,D_{2N+1})}$, and in some cases, supersymmetry enhancement to ${ m N}=2$. The authors construct Lagrangian descriptions for several AD theories, enabling exact computations of full superconformal indices and providing nontrivial checks via Coulomb-branch limits and S-duality. They also uncover IR dualities between distinct ${ m N}=1$ UV theories flowing to the same ${ m N}=2$ AD fixed points, and connect the enhancement patterns to 2d chiral algebras, saturating certain central-charge bounds. Overall, the paper advances a unified framework linking ${ m N}=1$ deformations, AD physics, and exact index calculations in a broad class of 4d SCFTs.

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.

Figures (1)

• Figure 1: IR duality among ${\cal N}=1$ theories. The IR fixed point is described by ${\cal N}=2$ AD theory