The Virtue of Defects in 4D Gauge Theories and 2D CFTs

Abstract

We advance a correspondence between the topological defect operators in Liouville and Toda conformal field theories - which we construct - and loop operators and domain wall operators in four dimensional N=2 supersymmetric gauge theories on S^4. Our computation of the correlation functions in Liouville/Toda theory in the presence of topological defect operators, which are supported on curves on the Riemann surface, yields the exact answer for the partition function of four dimensional gauge theories in the presence of various walls and loop operators; results which we can quantitatively substantiate with an independent gauge theory analysis. As an interesting outcome of this work for two dimensional conformal field theories, we prove that topological defect operators and the Verlinde loop operators are different descriptions of the same operators.

59 pages, latex; v2 corrections to some formulae

References in corpus (17)

• Liouville Correlation Functions from Four-dimensional Gauge Theories
• Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter
• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• Loop and surface operators in N=2 gauge theory and Liouville modular geometry
• Supersymmetric Boundary Conditions in N=4 Super Yang-Mills Theory
• Duality and defects in rational conformal field theory
• Gauge Theory Loop Operators and Liouville Theory
• The gravity duals of N=2 superconformal field theories
• Interface Yang-Mills, Supersymmetry, and Janus
• Fusion of conformal interfaces
• Loop operators and S-duality from curves on Riemann surfaces
• N=2 gauge theories and degenerate fields of Toda theory
• Quantum 't Hooft operators and S-duality in N=4 super Yang-Mills
• Perturbed Defects and T-Systems in Conformal Field Theory
• On the crossing relation in the presence of defects
• From Liouville to Chern-Simons, Alternative Realization of Wilson Loop Operators in AGT Duality
• Defects and Permutation branes in the Liouville field theory

Cited by in corpus (136)

• SUSY Gauge Theories on Squashed Three-Spheres
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• Exact Results in D=2 Supersymmetric Gauge Theories
• Bootstrapping the superconformal index with surface defects
• SL(2,R) Chern-Simons, Liouville, and Gauge Theory on Duality Walls
• Correlation Functions of Coulomb Branch Operators
• Seiberg-Witten Theories on Ellipsoids
• Exact Kahler Potential from Gauge Theory and Mirror Symmetry
• A & B model approaches to surface operators and Toda theories
• Walls, Lines, and Spectral Dualities in 3d Gauge Theories
• Deformed Prepotential, Quantum Integrable System and Liouville Field Theory
• On Three Dimensional Quiver Gauge Theories and Integrability
• Proving AGT conjecture as HS duality: extension to five dimensions
• On AGT Relations with Surface Operator Insertion and Stationary Limit of Beta-Ensembles
• Instanton counting with a surface operator and the chain-saw quiver
• Exact Results for 't Hooft Loops in Gauge Theories on S^4
• Dual Boundary Conditions in 3d SCFT's
• Defects in Jackiw-Teitelboim Quantum Gravity
• A direct proof of AGT conjecture at beta = 1
• Matrix model version of AGT conjecture and generalized Selberg integrals
• Infrared Computations of Defect Schur Indices
• Elliptic hypergeometry of supersymmetric dualities II. Orthogonal groups, knots, and vortices
• Anyonic Chains, Topological Defects, and Conformal Field Theory
• Braids, Walls, and Mirrors
• Proving the AGT relation for N_f = 0,1,2 antifundamentals
• SUSY monopole potentials in 2+1 dimensions
• 3d Chern-Simons Theory from M5-branes
• An E7 Surprise
• M2-brane surface operators and gauge theory dualities in Toda
• Coulomb Branch Operators and Mirror Symmetry in Three Dimensions
• Bekenstein-Hawking Entropy as Topological Entanglement Entropy
• Supersymmetric Casimir Energy and the Anomaly Polynomial
• Affine sl(N) conformal blocks from N=2 SU(N) gauge theories
• Exact results for Wilson loops in arbitrary representations
• Non-perturbative Defect One-Point Functions in Planar $\mathcal{N}=4$ Super-Yang-Mills
• A worldsheet extension of O(d,d;Z)
• CFT duals of three-dimensional de Sitter gravity
• Localization of 3d $\mathcal{N}=2$ Supersymmetric Theories on $S^1\times D^2$
• Large N Correlation Functions in Superconformal Field Theories
• Surface Defect, Anomalies and $b$-Extremization
• Brezin-Gross-Witten model as "pure gauge" limit of Selberg integrals
• The Superconformal Index of the (2,0) Theory with Defects
• Semiclassical Analysis of the 3d/3d Relation
• Wilson Loops in N=2 Superconformal Yang-Mills Theory
• Duality walls and defects in 5d N=1 theories
• Aspects of Defects in 3d-3d Correspondence
• Lorentzian Dynamics and Factorization Beyond Rationality
• The superconformal index and an elliptic algebra of surface defects
• Line Defects, Tropicalization, and Multi-Centered Quiver Quantum Mechanics
• Central Charges of 2d Superconformal Defects
• The Liouville side of the Vortex
• Gauge Theory Wilson Loops and Conformal Toda Field Theory
• Large N Free Energy of 3d N=4 SCFTs and AdS/CFT
• Holographic and Localization Calculations of Boundary F for $\mathcal{N}=4$ SUSY Yang-Mills Theory
• A slow review of the AGT correspondence
• Topological Field Theory with Haagerup Symmetry
• N=2 gauge theories on the hemisphere $H{S}^4$
• Monodromy Defects in Free Field Theories
• Boundary F-maximization
• Analysis of correlation functions in Toda theory and AGT-W relation for SU(3) quiver
• Superconformal Index with Duality Domain Wall
• Non-Perturbative Topological Strings And Conformal Blocks
• N=2 Generalized Superconformal Quiver Gauge Theory
• Hitchin Equation, Irregular Singularity, and $N=2$ Asymptotical Free Theories
• Higher laminations, webs and N=2 line operators
• Superconformal Index and 3d-3d Correspondence for Mapping Cylinder/Torus
• 't Hooft Operators in Gauge Theory from Toda CFT
• Classical conformal blocks from TBA for the elliptic Calogero-Moser system
• Generalized matrix models and AGT correspondence at all genera
• On W-algebras and the symmetries of defects of 6d N=(2,0) theory
• Line defects and (framed) BPS quivers
• Modular properties of characters of the W3 algebra
• W(1+infinity) algebra as a symmetry behind AGT relation
• 3d $\mathcal{N}=4$ Gauge Theories on an Elliptic Curve
• Degenerate operators in JT and Liouville (super)gravity
• Aspects of line operators of class S theories
• Classifying Superconformal Defects in Diverse Dimensions Part I: Superconformal Lines
• Supersymmetric D3/D5 for massive defects on curved space
• Circular Wilson loops in defect Conformal Field Theory
• Green-Schwarz Automorphisms and 6D SCFTs
• Network, Cluster coordinates and N=2 theory I
• A note on entanglement entropy for topological interfaces in RCFTs
• The classifying algebra for defects
• Non-Perturbative Defects in Tensor Models from Melonic Trees
• Comments on knotted 1/2 BPS Wilson loops
• Triality in SU(2) Seiberg-Witten theory and Gauss hypergeometric function
• A review on SUSY gauge theories on $S^3$
• Refined 3d-3d Correspondence
• Bootstrapping string dynamics in the 6d $\mathcal{N}=(2,0)$ theories
• AGT/Z${}_2$
• (de)Tails of Toda CFT
• Conformal Janus on Euclidean Sphere
• On Higgs Branch Localization of Seiberg-Witten Theories on Ellipsoid
• Complex saddles of three-dimensional de Sitter gravity via holography
• Boundary conditions in Toda theories and minimal models
• Non-Invertible Symmetry in Calabi-Yau Conformal Field Theories
• BPS states in the Minahan-Nemeschansky E6 theory
• The BPS Spectrum Generator In 2d-4d Systems
• A note on Wilson-'t Hooft operators
• Hartle-Hawking state and its factorization in 3d gravity
• Localization principle in SUSY gauge theories
• Localization of a supersymmetric gauge theory in the presence of a surface defect
• 6j symbols for the modular double, quantum hyperbolic geometry, and supersymmetric gauge theories
• Defects, Super-Poincaré line bundle and Fermionic T-duality
• Gluing I: Integrals and Symmetries
• The Schwarzian sector of higher spin CFTs
• Asymptotic M5-brane entropy from S-duality
• On classical and semiclassical properties of the Liouville theory with defects
• BPS states in the Omega-background and torus knots
• Janus interface entropy and Calabi's diastasis in four-dimensional $\mathcal{N}=2$ superconformal field theories
• Little String Origin of Surface Defects
• Duality walls in the 4d N=2 SU(N) gauge theory with 2N flavours
• Defect Partition Function from TDLs in Commutant Pairs
• Holographic Entropy and Calabi's Diastasis
• S-duality wall of SQCD from Toda braiding
• Additivity, Haag duality, and non-invertible symmetries
• OPE of Wilson-'t Hooft operators in N=4 and N=2 SYM with gauge group G=PSU(3)
• Comments on fusion matrix in N=1 super Liouville field theory
• Wilson Loop Invariants from $W_N$ Conformal Blocks
• Holographic Wilson Loops, Dielectric Interfaces, and Topological Insulators
• Describing codimension two defects
• Exact results and Schur expansions in quiver Chern-Simons-matter theories
• Open Verlinde line operators
• Wilson punctured network defects in 2D q-deformed Yang-Mills theory
• Note on refined topological vertex, Jack polynomials and instanton counting
• S-move matrix in the NS sector of $N=1$ super Liouville field theory
• Positive representations, multiplier Hopf algebra, and continuous canonical basis
• More on 't Hooft loops in N=4 SYM
• Interface entropy in four dimensions as Calabi's diastasis on the conformal manifold
• Double-Janus Linear Sigma Models and Generalized Reciprocity for Gauss Sums
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• Reconstructing the boundary of AdS from an infrared defect
• A note on W symmetry of N=2 gauge theory
• Schur Connections: Chord Counting, Line Operators, and Indices
• The quantum UV-IR map for line defects in $\mathfrak{gl}(3)$-type class $S$ theories
• Factorization and global symmetries in holography