N = 1 $$ \mathcal{N}=1 $$ deformations and RG flows of N = 2 $$ \mathcal{N}=2 $$ SCFTs

Abstract

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.

Supersymmetric Gauge Theories with Decoupled Operators and Chiral Ring Stability

“…This makes it possible to perform all usual computations, and to compactify on a circle. We concentrate on a duality between an N = 1 SU (2) gauge theory and the N = 2 A3 Argyres-Douglas [1,2], mapping the moduli space and chiral ring of the completed N = 1 theory to those of the A3 model. We reduce the completed gauge theory to 3d, finding a 3d duality with N = 4 SQED with two flavors.…”

“…Similarly, partition functions are computed dividing by the contribution of a chiral field with R-charge R [O]. Using these recipes, the leftover interacting sector in (1) was argued to be dual to A 3 AD theory, with α 0 mapping to the Coulomb branch generator [2]. …”

“…We check the validity of our proposal focusing on a class of theories in four dimensions recently discovered in [1,2,7]: certain N = 1 gauge theories exhibit unitarity bound violations, the interacting sector is proposed to be equivalent to a well-known class of N = 2 SCFT's called Argyres-Douglas (AD) theories [8][9][10][11], which cannot have a manifestly N = 2 lagrangian description.…”

“…We focus on a simple case, the A 3 AD theory, which admits an N = 1 lagrangian description in terms of an SU (2) gauge theory with an adjoint and two doublets [2].…”

“…First we point out that the superpotential as written in [2,7] are inconsistent: a superpotential term must be discarded, in order to satisfy a chiral ring stability criterion as in [12]. Our consistent superpotential displays the correct global symmetry and allows to map the moduli space of vacua and the chiral ring across the duality.…”