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.

We continue to investigate the N = 1 deformations of four-dimensional N = 2 superconformal field theories (SCFTs) labeled by a nilpotent element of the flavor symmetry [1]. This triggers a renormalization group (RG) flow to an N = 1 SCFT. We systematically analyze all possible deformations of this type for certain classes of 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 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 N = 1 theories where the fixed point is described by an 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.

We study aspects of the vertex operator algebra (VOA) corresponding to Argyres-Douglas (AD) theories engineered using the 6d N = (2, 0) theory of type J on a punctured sphere. We denote the AD theories as (and Y represent an irregular and a regular singularity respectively. We restrict to the 'minimal' case where J b [k] has no associated mass parameters, and the theory does not admit any exactly marginal deformations. The VOA corresponding to the AD theory is conjectured to be the Walgebra W k 2d (J, Y ), where k 2d = −h + b b+k with h being the dual Coxeter number of J. We verify this conjecture by showing that the Schur index of the AD theory is identical to the vacuum character of the corresponding VOA, and the Hall-Littlewood index computes the Hilbert series of the Higgs branch. We also find that the Schur and Hall-Littlewood index for the AD theory can be written in a simple closed form for b = h. We also test the conjecture that the associated variety of such VOA is identical to the Higgs branch. The M5-brane construction of these theories and the corresponding TQFT structure of the index play a crucial role in our computations.

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 S and some of rank-one SCFTs, where the deformation gives genuine N = 1 fixed points.