3d-3d correspondence revisited

  • Hee-Joong Chung
  • Tudor Dimofte
  • Sergei Gukov
  • Piotr Sułkowski
Open Access
Regular Article - Theoretical Physics

Abstract

In fivebrane compactifications on 3-manifolds, we point out the importance of all flat connections in the proper definition of the effective 3d \( \mathcal{N}=2 \) theory. The Lagrangians of some theories with the desired properties can be constructed with the help of homological knot invariants that categorify colored Jones polynomials. Higgsing the full 3d theories constructed this way recovers theories found previously by Dimofte-Gaiotto-Gukov. We also consider the cutting and gluing of 3-manifolds along smooth boundaries and the role played by all flat connections in this operation.

Keywords

Supersymmetric gauge theory Topological Field Theories Chern-Simons Theories Supersymmetry and Duality 

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Copyright information

© The Author(s) 2016

Authors and Affiliations

  • Hee-Joong Chung
    • 1
  • Tudor Dimofte
    • 2
  • Sergei Gukov
    • 1
    • 3
  • Piotr Sułkowski
    • 1
    • 4
  1. 1.California Institute of TechnologyPasadenaU.S.A.
  2. 2.Institute for Advanced StudyPrincetonU.S.A.
  3. 3.Max-Planck-Institut für MathematikBonnGermany
  4. 4.Faculty of PhysicsUniversity of WarsawWarsawPoland

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