(0,4) dualities

Abstract

We study a class of two-dimensional N = (0, 4) quiver gauge theories that flow to superconformal field theories. We find dualities for the superconformal field theories similar to the 4d N = 2 theories of class S, labelled by a Riemann surface C. The dual descriptions arise from various pair-of-pants decompositions, that involve an analog of the T N theory. Especially, we find the superconformal indices of such theories can be written in terms of a topological field theory on C. We interpret this class of SCFTs as the ones coming from compactifying 6d N = (2, 0) theory on CP 1 ×C. Moreover, some new dualities of (0, 2) and (2, 2) theories are also discussed.

On the reduction of 4d N = 1 $$ \mathcal{N}=1 $$ theories on S 2 $$ {\mathbb{S}}^2 $$

“…The 4d duality implies the genus is symmetric under c ↔ d, or, in more standard notation, that the U(1) B baryon symmetry maps to itself with a change of sign, with all other flavor symmetries fixed. This gives evidence for a N = (2, 2) duality, which was noticed also in [23]. Note that, since the theories have N = (2, 2) supersymmetry, we can also compute their S 2 partition functions as a function of twisted masses for the flavor symmetries, which comprises an independent check of this duality.…”

“…As in the N = (2, 2) case, the flavor symmetry 1 2 (R − r) gives rise to a subgroup of the extended R-symmetry group of (0, 4). In this reduction we obtain the theories considered in [23], which were observed to be N = (0, 4) sigma models with target space (a certain bundle over) the Higgs branch of the 4d theory. In the case of the E 6 theory, the N = 1 Lagrangian discussed in [24] gives rise upon reduction to an N = (0, 2) Lagrangian which flows to the N = (0, 4) reduction of the E 6 theory, and this was checked to have the expected E 6 symmetry in [24].…”

N $$ \mathcal{N} $$ =1 Lagrangians for generalized Argyres-Douglas theories

“…It should be possible to push the dimensional reduction further to two dimensions along the lines of [32,42,[61][62][63][64].…”

Superconformal index, BPS monodromy and chiral algebras

“…When N = 0, the twisted theory preserves N = (2, 2) SUSY in 2d. When N = −2, it preserves N = (0, 4) SUSY in 2d [25] and it has been considered in [26]. See appendix A for details.…”

“…It can be also written as 26) where r is the dimension of the Coulomb branch and R i are the dimension of the Coulomb branch operators. The r.h.s.…”