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3d-3d correspondence

Contents

Context

Duality in string theory

String theory

Contents

Idea

A duality in string theory: relation between the 3d superconformal worldvolume quantum field theory on M5-brane wrapped on a (hyperbolic) 3-manifold and 3d Chern-Simons theory/analytically continued Chern-Simons theory.

Properties

Relation to volume conjecture

In Gang-Kim-Lee 14b, 3.2, Gang-Kim 18 (21) it is argued that the volume conjecture for Chern-Simons theory on hyperbolic 3-manifolds Σ 3\Sigma^3 is the combined statement of two dualities in string theory

  1. AdS/CFT duality

  2. 3d-3d correspondence

for the situation of M5-branes wrapped on Σ 3\Sigma^3 (DGKV 10):

Wrapping the M5-brane on a torsion 3-cycle yields: fractional M2-brane.

Wrapping the M5-brane instead on a 2-manifold yields: AGT correspondence.

References

General

Original articles include

Review is in

Relation of the AGT-correspondence to the D=6 N=(2,0) SCFT and the 3d-3d correspondence:

Black 5-branes and AdS/CFT

Discussion of D=11 N=1 supergravity solutions for the near horizon geometry of black M5-branes wrapped on hyperbolic 3-manifolds Σ 3=H 3/Γ\Sigma^3 = H^3/\Gamma:

  • Aristomenis Donos, Jerome Gauntlett, Nakwoo Kim, Oscar Varelam, Wrapped M5-branes, consistent truncations and AdS/CMT, JHEP 1012:003, 2010 (arXiv:1009.3805)

  • Dongmin Gang, Nakwoo Kim, Sangmin Lee, Holography of Wrapped M5-branes and Chern-Simons theory, Physics Letters B Volume 733, 2 June 2014, Pages 316-319 (arXiv:1401.3595)

  • Dongmin Gang, Nakwoo Kim, Sangmin Lee, Holography of 3d-3d correspondence at Large NN, JHEP04(2015) 091 (arXiv:1409.6206)

  • Dongmin Gang, Nakwoo Kim, Large NN twisted partition functions in 3d-3d correspondence and Holography, Phys. Rev. D 99, 021901 (2019) (arXiv:1808.02797)

  • Dongmin Gang, Nakwoo Kim, Leopoldo A. Pando Zayas, Precision Microstate Counting for the Entropy of Wrapped M5-branes (arXiv:1905.01559)

Relation to volume conjecture

Discussion of the volume conjecture by combining the 3d/3d correspondence with AdS/CFT in these backgrounds:

Enhanced to a defect field theory:

  • Dongmin Gang, Nakwoo Kim, Mauricio Romo, Masahito Yamazaki, Aspects of Defects in 3d-3d Correspondence, J. High Energ. Phys. (2016) (arXiv:1510.05011)

Knot invariants

For discussion of knot invariants:

Entropy computation

Applied to computation of Bekenstein-Hawking entropy for black holes in string theory:

Last revised on October 9, 2019 at 12:03:13. See the history of this page for a list of all contributions to it.