Aspects of Defects in 3d-3d Correspondence

Abstract

In this paper we study supersymmetric co-dimension 2 and 4 defects in the compactification of the 6d $(2,0)$ theory of type $A_{N-1}$ on a 3-manifold $M$. The so-called 3d-3d correspondence is a relation between complexified Chern-Simons theory (with gauge group $SL(N,\mathbb{C})$) on $M$ and a 3d $\mathcal{N}=2$ theory $T_N[M]$. We establish a dictionary for this correspondence in the presence of supersymmetric defects, which are knots/links inside the 3-manifold. Our study employs a number of different methods: state-integral models for complex Chern-Simons theory, cluster algebra techniques, domain wall theory $T[SU(N)]$, 5d $\mathcal{N}=2$ SYM, and also supergravity analysis through holography. These methods are complementary and we find agreement between them. In some cases the results lead to highly non-trivial predictions on the partition function. Our discussion includes a general expression for the cluster partition function, in particular for non-maximal punctures and $N>2$. We also highlight the non-Abelian description of the 3d $\mathcal{N}=2$ $T_N[M]$ theory with defect included, as well as its Higgsing prescription and the resulting `refinement' in complex CS theory. This paper is a companion to our shorter paper arXiv:1510.03884, which summarizes our main results.

129 pages (sorry), 22 figures

References in corpus (20)

• Notes on SUSY Gauge Theories on Three-Sphere
• Supersymmetric Boundary Conditions in N=4 Super Yang-Mills Theory
• Holographic Wilson Loops
• The quantum dilogarithm and representations quantum cluster varieties
• Wilson Loops of Anti-symmetric Representation and D5-branes
• Defects and Quantum Seiberg-Witten Geometry
• Wrapped M5-branes, consistent truncations and AdS/CMT
• AGT on the S-duality Wall
• Quivers, YBE and 3-manifolds
• The Superconformal Index of the (2,0) Theory with Defects
• Emergent 3-manifolds from 4d Superconformal Indices
• Large N Free Energy of 3d N=4 SCFTs and AdS/CFT
• Holography of 3d-3d correspondence at Large N
• Boundaries and Defects of N=4 SYM with 4 Supercharges, Part I: Boundary/Junction Conditions
• 4d Quantum Geometry from 3d Supersymmetric Gauge Theory and Holomorphic Block
• Boundaries and Defects of N=4 SYM with 4 Supercharges, Part II: Brane Constructions and 3d N=2 Field Theories
• The moduli space of vacua of N=2 class S theories
• Taming Supersymmetric Defects in 3d-3d Correspondence
• Wilson loops on three-manifolds and their M2-brane duals
• BPS M5-branes as Defects for the 3d-3d Correspondence

Cited by in corpus (39)

• Three-dimensional $\mathcal{N}=2$ supersymmetric gauge theories and partition functions on Seifert manifolds: A review
• Rotating Black Hole Entropy from M5-branes
• Holographic Interfaces in N=4 SYM: Janus and J-folds
• Symmetry enhancement and closing of knots in 3d/3d correspondence
• Janus and J-fold Solutions from Sasaki-Einstein Manifolds
• A slow review of the AGT correspondence
• M-theoretic Genesis of Topological Phases
• Precision Microstate Counting for the Entropy of Wrapped M5-branes
• 3d dualities from 2d free field correlators: recombination and rank stabilization
• Non-unitary TQFTs from 3D $\mathcal{N}=4$ rank 0 SCFTs
• BPS Graphs: From Spectral Networks to BPS Quivers
• Supersymmetric Indices of 3d S-fold SCFTs
• 3d-3d correspondence for mapping tori
• All-Order Volume Conjecture for Closed 3-Manifolds from Complex Chern-Simons Theory
• Perturbative and nonperturbative aspects of complex Chern-Simons Theory
• Equivariant Verlinde algebra from superconformal index and Argyres-Seiberg duality
• The moduli spaces of S-fold CFTs
• Rethinking mirror symmetry as a local duality on fields
• Holographic Weyl Anomalies for 4d Defects in 6d SCFTs
• Variations on S-fold CFTs
• Refined 3d-3d Correspondence
• 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
• Marginal deformations and RG flows for type IIB S-folds
• On $\mathcal{N}=4$ supersymmetry enhancements in three dimensions
• Comments on Exchange Graphs in Cluster Algebras
• 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
• BPS Invariants for a Knot in Seifert Manifolds
• Mirror Symmetry and Mixed Chern-Simons Levels for Abelian 3d $\mathcal{N}=2$ theories
• Wilson punctured network defects in 2D q-deformed Yang-Mills theory
• Affine $\mathcal{W}$-algebras and Miura maps from 3d $\mathcal{N}=4$ non-Abelian quiver gauge theories
• Five-dimensional cohomological localization and squashed $q$-deformations of two-dimensional Yang-Mills theory
• Cluster-Enriched Yang-Baxter Equation from SUSY Gauge Theories
• S-folds and $Ad{S}_3$ flows from the D3-brane
• Double-Janus Linear Sigma Models and Generalized Reciprocity for Gauss Sums
• 3D-3D Correspondence from Seifert Fibering Operators
• Wrapped $M5$-branes and complex saddle points