Symmetry enhancement and closing of knots in 3d/3d correspondence

Abstract

We revisit Dimofte-Gaiotto-Gukov's construction of 3d gauge theories associated to 3-manifolds with a torus boundary. After clarifying their construction from a viewpoint of compactification of a 6d $\mathcal{N}=(2,0)$ theory of $A_1$-type on a 3-manifold, we propose a topological criterion for $SU(2)/SO(3)$ flavor symmetry enhancement for the $u(1)$ symmetry in the theory associated to a torus boundary, which is expected from the 6d viewpoint. Base on the understanding of symmetry enhancement, we generalize the construction to closed 3-manifolds by identifying the gauge theory counterpart of Dehn filling operation. The generalized construction predicts infinitely many 3d dualities from surgery calculus in knot theory. Moreover, by using the symmetry enhancement criterion, we show that theories associated to all hyperboilc twist knots have surprising $SU(3)$ symmetry enhancement which is unexpected from the 6d viewpoint.

57 pages, 9 figures, v2: some clarifications and references added

References in corpus (16)

• Notes on SUSY Gauge Theories on Three-Sphere
• Webs of five-branes and N=2 superconformal field theories
• Mirrors of 3d Sicilian theories
• Time-Reversal Breaking in QCD${}_4$, Walls, and Dualities in 2+1 Dimensions
• Generalized Volume Conjecture and the A-Polynomials -- the Neumann-Zagier Potential Function as a Classical Limit of Quantum Invariant
• Anomaly matching for phase diagram of massless ${\mathbb{Z}}_N$-QCD
• Circle compactification and 't Hooft anomaly
• SL(2,Z) Action On Three-Dimensional Conformal Field Theories With Abelian Symmetry
• C-P-T anomaly matching in bosonic quantum field theory and spin chains
• IR Dualities in General 3d Supersymmetric SU(N) QCD Theories
• Holography of 3d-3d correspondence at Large N
• Teichmuller TQFT vs Chern-Simons Theory
• Smallest 3d hyperbolic manifolds via simple 3d theories
• The moduli space of vacua of N=2 class S theories
• S-duality resurgence in SL(2) Chern-Simons theory
• Complex Chern-Simons theory at level k via the 3d-3d correspondence

Cited by in corpus (35)

• Mixed Anomalies, Two-groups, Non-Invertible Symmetries, and 3d Superconformal Indices
• Higher-Form Symmetries, Bethe Vacua, and the 3d-3d Correspondence
• Rotating Black Hole Entropy from M5-branes
• Three-dimensional gauge theories with supersymmetry enhancement
• $USp(2N_c)$ SQCD${}_3$ with antisymmetric: dualities and symmetry enhancements
• A slow review of the AGT correspondence
• M-theoretic Genesis of Topological Phases
• Precision Microstate Counting for the Entropy of Wrapped M5-branes
• A tale of exceptional 3d dualities
• Non-unitary TQFTs from 3D $\mathcal{N}=4$ rank 0 SCFTs
• Supersymmetric Indices of 3d S-fold SCFTs
• Large $N$ twisted partition functions in 3d-3d correspondence and Holography
• Generalized Symmetries and Anomalies of 3d N=4 SCFTs
• Chiral 3d SU(3) SQCD and N=2 mirror duality
• N=1 QED in 2+1 dimensions: Dualities and enhanced symmetries
• Expanding 3d $\mathcal{N}=2$ Theories around the Round Sphere
• Star shaped quivers with flux
• Marginal operators and supersymmetry enhancement in 3d $S$-fold SCFTs
• On $\mathcal{N}=4$ supersymmetry enhancements in three dimensions
• Adjoint Reidemeister torsions from wrapped M5-branes
• Infrared phases of 3D Class R theories
• Comments on Global Symmetries and Anomalies of $5d$ SCFTs
• A non-unitary bulk-boundary correspondence: Non-unitary Haagerup RCFTs from S-fold SCFTs
• 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
• (0,2) Dualities and the 4-Simplex
• Free field realisation of boundary vertex algebras for Abelian gauge theories in three dimensions
• Black holes and Large $N$ complex saddles in 3D-3D correspondence
• Five loop renormalization of the Wess-Zumino model
• Compactifying 5d superconformal field theories to 3d
• Magnetically charged AdS5 black holes from class S theories on hyperbolic 3-manifolds
• Non-hyperbolic 3-manifolds and 3D field theories for 2D Virasoro minimal models
• Quantum Approach to Dehn Surgery Problem
• 3D-3D Correspondence from Seifert Fibering Operators
• Aspects of 4d supersymmetric dynamics and geometry