Abstract
We study certain mathcal{N}=1 preserving deformations of four-dimensional mathcal{N}=2 superconformal field theories (SCFTs) with non-abelian flavor symmetry. The deformation is described by adding an mathcal{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 mathcal{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 (A1, An) Argyres-Douglas theories. From these “Lagrangian descriptions,” we compute the full superconformal indices of the (A1, An) theories and find agreements with the previous results. Furthermore, we study the cases, including the TN and R0,N theories of class mathcal{S} and some of rank-one SCFTs, where the deformation gives genuine mathcal{N}=1 fixed points.
Highlights
Is described as follows: suppose we have an N = 2 superconformal field theories (SCFTs), T, with a non-Abelian flavor symmetry F
We study certain N = 1 preserving deformations of four-dimensional N = 2 superconformal field theories (SCFTs) with non-abelian flavor symmetry
We notice that there is an additional Z2 label to the puncture and the pair of pants, which we denote as σp = ±1 and σb = ±1. It was found in [28] that the four-dimensional description corresponding to the σp = −1 maximal puncture attached to the σb = +1 pair of pants is to add the chiral multiplet M transforming in the adjoint representation of the SU(N ) flavor symmetry, and the superpotential coupling TrM μ
Summary
We apply the general argument in the previous section to a family of SCFTs of Argyres-Douglas type with an SU(N ) flavor symmetry. An N = 2 SCFT with Coulomb branch operators with fractional dimensions is called as (a generalized) Argyres-Douglas theory. They span the Coulomb branch of the theory In the latter case we have a mass parameter with dimension 1 associated to a U(1) global symmetry. This class of theories has the SU(2) flavor symmetry whose conserved current multiplet has a moment map operator μ as a lowest component, and a corresponding mass parameter of dimension 1. We will focus here on the special case where k = N m + N + 1 In this case, the dimensions of the Coulomb branch operators are. We seem to have one missing and one superfluous B multiplet in this analysis to completely match with the Coulomb branch multiplets in the (A1, A2n) theory. It is not clear to us from here, how the superfluous operator decouple and the missing one appears along the RG flow
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