3d Chern-Simons Theory from M5-branes

Abstract

We study 5d N=2 maximally supersymmetric Yang-Mills theory with a gauge group G on S^2 x M_3, where M_3 is a 3-manifold. By explicit localization computation we show that the path-integral of the 5d N=2 theory reduces to that of the 3d G_C Chern-Simons theory on M_3, where G_C is the complexification of G. This gives a direct derivation of the appearance of the Chern-Simons theory from the compactification of the 6d (2,0) theory, confirms the predictions from the 3d/3d correspondence for G=SU(N), and suggests the generalization of the correspondence to more general gauge groups.

28 pages, minor corrections and references added, comments on the gauge-fixing added. The version published in JHEP

References in corpus (7)

• Notes on SUSY Gauge Theories on Three-Sphere
• The 4d Superconformal Index from q-deformed 2d Yang-Mills
• AGT on the S-duality Wall
• 3d TQFT from 6d SCFT
• Quivers, YBE and 3-manifolds
• Emergent 3-manifolds from 4d Superconformal Indices
• Complex Chern-Simons from M5-branes on the Squashed Three-Sphere

Cited by in corpus (55)

• Ω-deformation and quantization
• Universal Spinning Black Holes and Theories of Class $\mathcal{R}$
• Rotating Black Hole Entropy from M5-branes
• Three-dimensional gauge theories with supersymmetry enhancement
• Symmetry enhancement and closing of knots in 3d/3d correspondence
• Supersymmetric Rényi Entropy in Five Dimensions
• Aspects of Defects in 3d-3d Correspondence
• Sequencing BPS Spectra
• A slow review of the AGT correspondence
• The general M5-brane superconformal index
• Supersymmetric gauge theory, (2,0) theory and twisted 5d Super-Yang-Mills
• Precision Microstate Counting for the Entropy of Wrapped M5-branes
• SymTFTs and Duality Defects from 6d SCFTs on 4-manifolds
• M-theoretic Genesis of Topological Phases
• Colored Kauffman Homology and Super-A-polynomials
• Holography of 3d-3d correspondence at Large N
• 3d-3d Correspondence Revisited
• Toda Theory From Six Dimensions
• Teichmuller TQFT vs Chern-Simons Theory
• Large $N$ twisted partition functions in 3d-3d correspondence and Holography
• 4d Quantum Geometry from 3d Supersymmetric Gauge Theory and Holomorphic Block
• Quiver gauge theories and integrable lattice models
• Perturbative and nonperturbative aspects of complex Chern-Simons Theory
• 5d Higgs Branch Localization, Seiberg-Witten Equations and Contact Geometry
• Chern-Simons theory from M5-branes and calibrated M2-branes
• Ω-deformation of B-twisted gauge theories and the 3d-3d correspondence
• Supersymmetric backgrounds from 5d N=1 supergravity
• Supersymmetric gauge theories on five-manifolds
• Surface defects as transfer matrices
• Rigid Supersymmetry on 5-dimensional Riemannian Manifolds and Contact Geometry
• A $\mathcal{N}=2$ Supersymmetric $Ad{S}_4$ Solution in M-theory with Purely Magnetic Flux
• Refined 3d-3d Correspondence
• Expanding 3d $\mathcal{N}=2$ Theories around the Round Sphere
• Indices for 6 dimensional superconformal field theories
• 3d $\mathcal{N}=2$ minimal SCFTs from Wrapped M5-branes
• M5-branes on S^2 x M_4: Nahm's Equations and 4d Topological Sigma-models
• Taming Supersymmetric Defects in 3d-3d Correspondence
• BPS M5-branes as Defects for the 3d-3d Correspondence
• 3d Gravity as a random ensemble
• A non-unitary bulk-boundary correspondence: Non-unitary Haagerup RCFTs from S-fold SCFTs
• 5D SYM on 3D Deformed Spheres
• AGT relation in the light asymptotic limit
• Integrable 3D lattice model in M-theory
• Gauging and Decoupling in 3d $\mathcal{N}=2$ dualities
• Solving Mass-deformed Holography Perturbatively
• Equivariant U(N) Verlinde algebra from Bethe/Gauge correspondence
• Five-dimensional cohomological localization and squashed $q$-deformations of two-dimensional Yang-Mills theory
• Partition Functions of $\mathcal{N}=1$ Gauge Theories on $S^2\times {\mathbb{R}}_{\epsilon }^2$ and Duality
• Intersecting Surface defects and 3d Superconformal indices
• Four-Dimensional N=2 Supersymmetric Theory with Boundary as a Two-Dimensional Complex Toda Theory
• 3D-3D Correspondence from Seifert Fibering Operators
• Localization of four-dimensional super Yang-Mills theories compactified on Riemann surface
• The geometric Langlands twist in five and six dimensions
• Quantum Trilogy: Discrete Toda, Y-System and Chaos
• Wrapped $M5$-branes and complex saddle points