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 (37)

• Liouville Correlation Functions from Four-dimensional Gauge Theories
• N=2 dualities
• Localization of gauge theory on a four-sphere and supersymmetric Wilson loops
• An Index for 4 dimensional Super Conformal Theories
• Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter
• S-Duality of Boundary Conditions In N=4 Super Yang-Mills Theory
• Mirror Symmetry in Three Dimensional Gauge Theories
• Counting chiral primaries in N=1 d=4 superconformal field theories
• The Exact Superconformal R-Symmetry Extremizes Z
• Janus Configurations, Chern-Simons Couplings, And The Theta-Angle in N=4 Super Yang-Mills Theory
• Notes on SUSY Gauge Theories on Three-Sphere
• Supersymmetric Boundary Conditions in N=4 Super Yang-Mills Theory
• The complete superconformal index for N=6 Chern-Simons theory
• Index for three dimensional superconformal field theories with general R-charge assignments
• Nonperturbative Tests of Three-Dimensional Dualities
• The Virtue of Defects in 4D Gauge Theories and 2D CFTs
• Gauge Theory Loop Operators and Liouville Theory
• SL(2,R) Chern-Simons, Liouville, and Gauge Theory on Duality Walls
• The dual of Janus -:- an interface CFT
• Generalized Superconformal Index for Three Dimensional Field Theories
• Interface Yang-Mills, Supersymmetry, and Janus
• Superconformal indices of three-dimensional theories related by mirror symmetry
• Exact Results for 't Hooft Loops in Gauge Theories on S^4
• Three dimensional Janus and time-dependent black holes
• Loop operators and S-duality from curves on Riemann surfaces
• 3d Partition Function as Overlap of Wavefunctions
• AGT on the S-duality Wall
• 3-Manifolds and 3d Indices
• Line Operator Index on S1 $\times$ S3
• Dynamics of N=2 Supersymmetric Chern-Simons Theories
• Semiclassical Analysis of the 3d/3d Relation
• Gauge Theories Labelled by Three-Manifolds
• Janus and Multifaced Supersymmetric Theories
• Janus and Multifaced Supersymmetric Theories II
• Chern-Simons Theory and S-duality
• 4D and 2D superconformal index with surface operator
• 6j symbols for the modular double, quantum hyperbolic geometry, and supersymmetric gauge theories

Cited by in corpus (22)

• Bootstrapping the superconformal index with surface defects
• Down the rabbit hole with theories of class S
• Dual Boundary Conditions in 3d SCFT's
• Localization of 3d $\mathcal{N}=2$ Supersymmetric Theories on $S^1\times D^2$
• The Superconformal Index of Class S Theories of Type D
• Supersymmetric Boundary Conditions in Three Dimensional N = 2 Theories
• A slow review of the AGT correspondence
• Vanishing superconformal indices and the chiral symmetry breaking
• Superconformal Index and 3d-3d Correspondence for Mapping Cylinder/Torus
• On 't Hooft Defects, Monopole Bubbling and Supersymmetric Quantum Mechanics
• 3d $\mathcal{N}=4$ Gauge Theories on an Elliptic Curve
• Dualities of Corner Configurations and Supersymmetric Indices
• Mirror symmetry of 3d $\mathcal{N}=4$ gauge theories and supersymmetric indices
• Bethe/Gauge correspondence in odd dimension: modular double, non-perturbative corrections and open topological strings
• On dimensional reduction of 4d N=1 Lagrangians for Argyres-Douglas theories
• Gluing I: Integrals and Symmetries
• Duality walls in the 4d N=2 SU(N) gauge theory with 2N flavours
• S-duality wall of SQCD from Toda braiding
• Deconstructing Defects
• Quarter-indices for basic ortho-symplectic corners
• Schur Connections: Chord Counting, Line Operators, and Indices
• Interface line operators in $\mathcal{N}=4$ SYM theories and supersymmetric indices