Mirror symmetry of 3D N=4 gauge theories and supersymmetric indices

Abstract

We compute supersymmetric indices to test mirror symmetry of three-dimensional N = 4 gauge theories and dualities of half-BPS enriched boundary conditions and interfaces in fourdimensional N = 4 Super Yang-Mills theory. We find the matching of indices as strong evidences for various dualities of the 3d interfaces conjectured by Gaiotto and Witten under the action of S-duality in Type IIB string theory.

Abelian dualities of $$ \mathcal{N} $$ = (0, 4) boundary conditions

“…In this paper we extend the duality network of 4d N = 4, 3d N = 4 and 2d N = (0, 4) gauge theories [31,32] by examining half-BPS N = (0, 4) boundary conditions in 3d N = 4 gauge theories that can be constructed from the brane setup in Type IIB string theory [22,35,31]. Unlike the cases studied in [31,32], the N = (0, 4) configurations discussed in this paper involve 3d N = 4 gauge theories with Neumann boundary condition N or/and 2d N = (0, 4) gauge theories. 3 Accordingly, as we argue in the main text, they need more careful treatment in the computation of supersymmetric indices.…”

“…This prescription is distinguished from the half-index of Dirichlet b.c. for 4d gauge theories [31,32]. The effective Chern-Simons coupling k eff encodes the total boundary U (1) ∂ and F anomalies in such a way that the boundary anomaly can be viewed as the exterior derivative of a Cherm-Simons form at level k eff [30].…”

“…More recently, [31] have presented dualities of half-BPS interfaces and quarter-BPS corner configurations in four-dimensional N = 4 SYM theory. Subsequently, [32] have shown more general dualities of half-BPS boundary conditions and interfaces in 4d N = 4 SYM theory conjectured by Gaiotto and Witten [5]. When the local operators are supported at two-dimensional boundary and corner configuration of superconformal field theories, one can embed the Vertex Operator Algebras (VOAs) into the algebras of local operators so that the correlation functions of certain protected operators are encoded in the VOAs [33,34].…”

“…In[31] the gauge symmetry stems from 4d gauge theories while in[32] it also results from 3d gauge theories.…”

Supersymmetric indices of 3d S-fold SCFTs

“…See, for example,[22,[31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47] for some recent work in 3d and 4d. See also[48] for a very recent paper that discussed supersymmetric indices of 3d N = 4 gauge theories.…”