N $$ \mathcal{N} $$ =1 Deformations and RG flows of N $$ \mathcal{N} $$ =2 SCFTs, part II: non-principal deformations

Abstract

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.

Testing Macdonald index as a refined character of chiral algebra

“…An N = 1 Lagrangian approach to the Argyres-Douglas theories has been developed since [42,43,44]. In this approach, one starts from a normal 4d N = 1 gauge theory with Lagrangian description, and surprisingly some special RG flow takes us to IR SCFT with enhanced supersymmetry, such as the AD theories.…”

Sequences of 6d SCFTs on generic Riemann surfaces

“…This means that the N copies of SU (2) symmetries corresponding to the minimal punctures get enhanced to U Sp(2N ) somewhere on the conformal manifold of the IR SCFT. 10 Now, with the trinion at hand we wish to combine several of them to form a higher genus Riemann surface. Since we already know how to glue the SU (2) N maximal punctures , here we will only specify how to glue the new U Sp(2N ) maximal punctures [11].…”

“…Much more is known for special surfaces. For example (2, 0) theories on surfaces with irregular punctures in some cases give Argyres-Douglas theories, for which Lagrangians have been worked out in [8][9][10]. Other examples involve (2, 0) SCFTs probing ADE singularities and higher rank E-string on surfaces of genus zero with at most two punctures or tori [11][12][13][14][15], some more esoteric 6d SCFTs on tori [16,17], as well as (2, 0) on spheres with special collections of punctures [7].…”

Supersymmetric Gauge Theories with Decoupled Operators and Chiral Ring Stability

“…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.…”

“…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.…”