Line Operator Index on S1 $\times$ S3

Abstract

We derive a general formula of an index for N = 2 superconformal field theories on S1 \times S3 with insertions of BPS Wilson line or 't Hooft line operator at the north pole and their anti-counterpart at the south pole of S3. One-loop and monopole bubbling effects are taken into account in the computation. As examples, we calculate the indices for N = 4 theories and N = 2 SU(2) theory with Nf = 4, and find good agreements between indices of line operators related by S-duality. The relation between Verlinde loop operators and the indices is explored. The holographic correspondence between the fundamental (anti-symmetric) Wilson line operator and the fundamental string (D5 brane) in AdS5\timesS5 is confirmed by the index comparison.

55 pages, 5 figures. v2:references added, sec 5.2, 5.3 are added, minor corrections

References in corpus (23)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Applications of the Superconformal Index for Protected Operators and q-Hypergeometric Identities to N=1 Dual Theories
• The 4d Superconformal Index from q-deformed 2d Yang-Mills
• Index for three dimensional superconformal field theories with general R-charge assignments
• Wilson Loops of Anti-symmetric Representation and D5-branes
• 4d Index to 3d Index and 2d TQFT
• From 4d superconformal indices to 3d partition functions
• Generalized Superconformal Index for Three Dimensional Field Theories
• Relation between the 4d superconformal index and the S^3 partition function
• Elliptic hypergeometry of supersymmetric dualities II. Orthogonal groups, knots, and vortices
• The Spectrum of Excitations of Holographic Wilson Loops
• On the Superconformal Index of N=1 IR Fixed Points: A Holographic Check
• Line operators on S^1xR^3 and quantization of the Hitchin moduli space
• 3-Manifolds and 3d Indices
• One-loop Effective Action of the Holographic Antisymmetric Wilson Loop
• Electric-Magnetic Duality And The Geometric Langlands Program
• Superconformal indices of $\mathcal{N}=4$ SYM field theories
• N=4 SYM on R x S^3 and Theories with 16 Supercharges
• Localization of N=4 Superconformal Field Theory on S^1 x S^3 and Index
• 't Hooft Operators in Gauge Theory from Toda CFT
• 4D and 2D superconformal index with surface operator
• The 1/2 BPS 't Hooft loops in N=4 SYM as instantons in 2d Yang-Mills
• Quantized Non-Abelian Monopoles on S^3

Cited by in corpus (42)

• Bootstrapping the superconformal index with surface defects
• Infrared Computations of Defect Schur Indices
• Coulomb Branch Operators and Mirror Symmetry in Three Dimensions
• The exact Schur index of $\mathcal{N}=4$ SYM
• The Superconformal Index of Class S Theories of Type D
• A review of the T_N theory and its cousins
• On a modular property of N=2 superconformal theories in four dimensions
• A slow review of the AGT correspondence
• Coulomb Branch Quantization and Abelianized Monopole Bubbling
• Brane bending and monopole moduli
• Superconformal Index with Duality Domain Wall
• The exact Schur index in closed form
• $\mathcal{N}=2^{\ast }$ Schur indices
• Vanishing superconformal indices and the chiral symmetry breaking
• Higher laminations, webs and N=2 line operators
• Superconformal Index and 3d-3d Correspondence for Mapping Cylinder/Torus
• 4d $\mathcal{N}=3$ indices via discrete gauging
• Scheme dependence of instanton counting in ALE spaces
• On 't Hooft Defects, Monopole Bubbling and Supersymmetric Quantum Mechanics
• The $\mathcal{N}=4$ Schur index with Polyakov loops
• Exact $\mathcal{N}=2^{\ast }$ Schur line defect correlators
• Aspects of line operators of class S theories
• Schur Indices of Class $\mathcal{S}$ and Quasimodular Forms
• Large $N$ and large representations of Schur line defect correlators
• An Index for Ray Operators in 5d $E_n$ SCFTs
• Orbifolds, Defects and Sphere Partition Function
• ABCD of 't Hooft operators
• Excitations of bubbling geometries for line defects
• Giant graviton expansions and ETW brane
• 5d gauge theories on orbifolds and 4d 't Hooft line indices
• Resumming perturbative series in the presence of monopole bubbling effects
• Orbifold ETW brane and half-indices
• Wilson punctured network defects in 2D q-deformed Yang-Mills theory
• ADHM Wilson line defect indices
• S-duality of boundary lines in $\mathcal{N}=4$ SYM theories and supersymmetric indices
• Abelian dualities and line defect indices for 3d gauge theories
• Connecting Localization and Wall-Crossing via D-Branes
• $\mathcal{N}=4$ line defect correlators of type BCD
• On Poisson geometry and supersymmetric sigma models
• Interface line operators in $\mathcal{N}=4$ SYM theories and supersymmetric indices
• Schur Connections: Chord Counting, Line Operators, and Indices
• Quarter-indices for basic ortho-symplectic corners