Superconformal Index with Duality Domain Wall

Abstract

We study a superconformal index for $\mathcal{N}=4$ super Yang-Mills on $S^1\times S^3$ with a half BPS duality domain wall inserted at the great two-sphere in $S^3$. The index is obtained by coupling the 3d generalized superconformal index on the duality domain wall with 4d half-indices. We further consider insertions of line operators to the configuration and propose integral equations which express that the 3d index on duality domain wall is a duality kernel relating half indices of two line operators related by the duality map. We explicitly check the proposed integral equations for various duality domain walls and line operators in the $\mathcal{N}=4$ SU(2) theory. We also briefly comment on a generalization to $\mathcal{N}=2$ $A_1$ Gaiotto theories with a simple example, $\mathcal{N}=2$ SU(2) SYM with four flavors.

v1: 25 pages, 4 figures. v2: comments and a reference added, minor corrections. v3: 30 pages, new results and discussions added to sec 4.5 and sec 5.1, eq 49 and eq 51 corrected, text improved; to appear in JHEP

References in corpus (9)

• Notes on SUSY Gauge Theories on Three-Sphere
• Supersymmetric Boundary Conditions in N=4 Super Yang-Mills Theory
• Generalized Superconformal Index for Three Dimensional Field Theories
• Interface Yang-Mills, Supersymmetry, and Janus
• Superconformal indices of three-dimensional theories related by mirror symmetry
• Loop operators and S-duality from curves on Riemann surfaces
• AGT on the S-duality Wall
• Janus and Multifaced Supersymmetric Theories II
• Chern-Simons Theory and S-duality