SL(2,R) Chern-Simons, Liouville, and Gauge Theory on Duality Walls

Abstract

We propose an equivalence of the partition functions of two different 3d gauge theories. On one side of the correspondence we consider the partition function of 3d SL(2,R) Chern-Simons theory on a 3-manifold, obtained as a punctured Riemann surface times an interval. On the other side we have a partition function of a 3d N=2 superconformal field theory on S^3, which is realized as a duality domain wall in a 4d gauge theory on S^4. We sketch the proof of this conjecture using connections with quantum Liouville theory and quantum Teichmuller theory, and study in detail the example of the once-punctured torus. Motivated by these results we advocate a direct Chern-Simons interpretation of the ingredients of (a generalization of) the Alday-Gaiotto-Tachikawa relation. We also comment on M5-brane realizations as well as on possible generalizations of our proposals.

53+1 pages, 14 figures; v2: typos corrected, references added

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Cited by in corpus (115)

• Bootstrapping the superconformal index with surface defects
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• Factorisation of N = 2 theories on the squashed 3-sphere
• Walls, Lines, and Spectral Dualities in 3d Gauge Theories
• Superpolynomials for toric knots from evolution induced by cut-and-join operators
• Dual Boundary Conditions in 3d SCFT's
• Elliptic hypergeometry of supersymmetric dualities II. Orthogonal groups, knots, and vortices
• Gauge Theories on ALE Space and Super Liouville Correlation Functions
• Ω-deformation and quantization
• 3d Chern-Simons Theory from M5-branes
• Solving 3d Gravity with Virasoro TQFT
• 3d TQFT from 6d SCFT
• Holographic duals of 3d S-fold CFTs
• 3d analogs of Argyres-Douglas theories and knot homologies
• Higher-Form Symmetries, Bethe Vacua, and the 3d-3d Correspondence
• Quivers, YBE and 3-manifolds
• Universal Spinning Black Holes and Theories of Class $\mathcal{R}$
• Non-Abelian Localization for Supersymmetric Yang-Mills-Chern-Simons Theories on Seifert Manifold
• Three-dimensional gauge theories with supersymmetry enhancement
• The $Ad{S}_5$ non-Abelian T-dual of Klebanov-Witten as a $\mathcal{N}=1$ linear quiver from M5-branes
• Semiclassical Analysis of the 3d/3d Relation
• Holographic Interfaces in N=4 SYM: Janus and J-folds
• Supersymmetric Boundary Conditions in Three Dimensional N = 2 Theories
• Aspects of Defects in 3d-3d Correspondence
• Peacock patterns and new integer invariants in topological string theory
• The superconformal index and an elliptic algebra of surface defects
• On 3d extensions of AGT relation
• Emergent 3-manifolds from 4d Superconformal Indices
• Taming Defects in $\mathcal{N}=4$ Super-Yang-Mills
• Network and Seiberg Duality
• Sequencing BPS Spectra
• Large N Free Energy of 3d N=4 SCFTs and AdS/CFT
• Janus and J-fold Solutions from Sasaki-Einstein Manifolds
• A slow review of the AGT correspondence
• Precision Microstate Counting for the Entropy of Wrapped M5-branes
• M-theoretic Genesis of Topological Phases
• S-duality as a beta-deformed Fourier transform
• Colored Kauffman Homology and Super-A-polynomials
• Superconformal Index with Duality Domain Wall
• Holography of 3d-3d correspondence at Large N
• Boundaries and Defects of N=4 SYM with 4 Supercharges, Part I: Boundary/Junction Conditions
• 3d dualities from 2d free field correlators: recombination and rank stabilization
• Non-unitary TQFTs from 3D $\mathcal{N}=4$ rank 0 SCFTs
• 3d-3d Correspondence Revisited
• Teichmuller TQFT vs Chern-Simons Theory
• BPS Graphs: From Spectral Networks to BPS Quivers
• Superconformal Index and 3d-3d Correspondence for Mapping Cylinder/Torus
• Large $N$ twisted partition functions in 3d-3d correspondence and Holography
• 3d-3d correspondence for mapping tori
• Supersymmetric Indices of 3d S-fold SCFTs
• A 5d/3d duality from relativistic integrable system
• Quiver gauge theories and integrable lattice models
• All-Order Volume Conjecture for Closed 3-Manifolds from Complex Chern-Simons Theory
• $q$-Virasoro modular double and 3d partition functions
• Perturbative and nonperturbative aspects of complex Chern-Simons Theory
• Chern-Simons theory from M5-branes and calibrated M2-branes
• Holography of Wrapped M5-branes and Chern-Simons theory
• Ω-deformation of B-twisted gauge theories and the 3d-3d correspondence
• Equivariant Verlinde algebra from superconformal index and Argyres-Seiberg duality
• The moduli spaces of S-fold CFTs
• A 3d-3d appetizer
• Basic hypergeometry of supersymmetric dualities
• Abelian dualities of $\mathcal{N}=(0,4)$ boundary conditions
• S-duality resurgence in SL(2) Chern-Simons theory
• Surface defects as transfer matrices
• Rethinking mirror symmetry as a local duality on fields
• Janus configurations with SL(2,Z)-duality twists, Strings on Mapping Tori, and a Tridiagonal Determinant Formula
• Holographic Weyl Anomalies for 4d Defects in 6d SCFTs
• A $\mathcal{N}=2$ Supersymmetric $Ad{S}_4$ Solution in M-theory with Purely Magnetic Flux
• Dimer Models, Integrable Systems and Quantum Teichmuller Space
• Variations on S-fold CFTs
• Expanding 3d $\mathcal{N}=2$ Theories around the Round Sphere
• An $\mathcal{N}=1$ 3d-3d Correspondence
• Hyperbolic 3-manifolds and Cluster Algebras
• 3d $\mathcal{N}=2$ minimal SCFTs from Wrapped M5-branes
• Marginal operators and supersymmetry enhancement in 3d $S$-fold SCFTs
• Symmetry enhancement and duality walls in 5d gauge theories
• M5-branes on S^2 x M_4: Nahm's Equations and 4d Topological Sigma-models
• On $\mathcal{N}=4$ supersymmetry enhancements in three dimensions
• Marginal deformations and RG flows for type IIB S-folds
• Taming Supersymmetric Defects in 3d-3d Correspondence
• Challenges of beta-deformation
• 3d Gravity as a random ensemble
• On Integrable Structure and Geometric Transition in Supersymmetric Gauge Theories
• Static Charges in the Low-Energy Theory of the S-Duality Twist
• Infrared phases of 3D Class R theories
• Localization principle in SUSY gauge theories
• A non-unitary bulk-boundary correspondence: Non-unitary Haagerup RCFTs from S-fold SCFTs
• Condensates and instanton - torus knot duality. Hidden Physics at UV scale
• Duality walls in the 4d N=2 SU(N) gauge theory with 2N flavours
• Generalized non-unitary Haagerup-Izumi modular data from 3D S-fold SCFTs
• Integral pentagon relations for 3d superconformal indices
• Gauging and Decoupling in 3d $\mathcal{N}=2$ dualities
• Entanglement in Theory Space
• S-duality wall of SQCD from Toda braiding
• Equivariant U(N) Verlinde algebra from Bethe/Gauge correspondence
• (0,2) Dualities and the 4-Simplex
• Black holes and Large $N$ complex saddles in 3D-3D correspondence
• Mirror Symmetry and Mixed Chern-Simons Levels for Abelian 3d $\mathcal{N}=2$ theories
• Affine $\mathcal{W}$-algebras and Miura maps from 3d $\mathcal{N}=4$ non-Abelian quiver gauge theories
• Ground States of Duality-twisted Sigma-Models with K3 Target Space
• Topological Aspects of Matters and Langlands Program
• 3d $\mathcal{N}=2$ Brane Webs and Quiver Matrices
• S-folds and $Ad{S}_3$ flows from the D3-brane
• The Virasoro fusion kernel and Ruijsenaars' hypergeometric function
• Non-hyperbolic 3-manifolds and 3D field theories for 2D Virasoro minimal models
• Magnetically charged AdS5 black holes from class S theories on hyperbolic 3-manifolds
• The colored Jones polynomials as vortex partition functions
• Disk, interval, point: on constructions of quantum field theories with holomorphic action functionals
• Double-Janus Linear Sigma Models and Generalized Reciprocity for Gauss Sums
• Resurgence in complex Chern-Simons theory at generic levels
• 3D-3D Correspondence from Seifert Fibering Operators
• Quantum Trilogy: Discrete Toda, Y-System and Chaos
• Wrapped $M5$-branes and complex saddle points
• QFT Realization of Non-Unitary $\mathfrak{sl}(2,\mathbb{C})$ WRT Invariants and Their Galois Conjugations