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3d-3d Correspondence and 2d $\mathcal{N}=(0,2)$ Boundary Conditions

Hee-Joong Chung

Abstract

We consider quiver forms that appear in the motivic Donaldson-Thomas generating series or characters of conformal field theories and relate them to 3d $\mathcal{N}=2$ theories on $D^2 \times_q S^1$ with certain boundary conditions preserving 2d $\mathcal{N}=(0,2)$ supersymmetry. We apply this to the 3d-3d correspondence and provide a Lagrangian description of 3d $\mathcal{N}=2$ theories $T[M_3]$ with 2d $\mathcal{N}=(0,2)$ boundary conditions for 3-manifolds $M_3$ in several contexts.

3d-3d Correspondence and 2d $\mathcal{N}=(0,2)$ Boundary Conditions

Abstract

We consider quiver forms that appear in the motivic Donaldson-Thomas generating series or characters of conformal field theories and relate them to 3d theories on with certain boundary conditions preserving 2d supersymmetry. We apply this to the 3d-3d correspondence and provide a Lagrangian description of 3d theories with 2d boundary conditions for 3-manifolds in several contexts.
Paper Structure (17 sections, 106 equations)

This paper contains 17 sections, 106 equations.

Table of Contents

  1. Introduction
  2. Quiver forms and 3d $\mathcal{N}=2$ theories
  3. Donaldson-Thomas invariant for symmetric quiver and quiver form
  4. 2d $\mathcal{N}=(0,2)$ boundary conditions of 3d $\mathcal{N}=2$ theories
  5. Quiver form and Dirichlet boundary conditions
  6. 3d-3d correspondence and quiver forms
  7. 3d $\mathcal{N}=2$ theory for knot conormal $L_K$
  8. 3d $\mathcal{N}=2$ theory for knot complement and surgery
  9. 3d $\mathcal{N}=2$ theory for $a$-deformed homological block $F_K$
  10. The case of $G=SU(2)$ and surgery
  11. 3d $\mathcal{N}=2$ theory for closed 3-manifold and logarithmic CFT
  12. Orientation reversal of 3-manifold
  13. 3d-3d correspondence for Jones polynomial
  14. Quiver forms and refinement
  15. 3d $\mathcal{N}=2$ theory for Jones polynomial of twist and torus knots
  16. ...and 2 more sections