nLab 3d-3d correspondence



Duality in string theory

String theory



A duality in string theory: relation between the D=3 N=2 SYM worldvolume quantum field theory on M5-brane wrapped on a (hyperbolic) 3-manifold and 3d Chern-Simons theory/analytically continued Chern-Simons theory.


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):

graphics from Sati-Schreiber 19c

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.



Original articles include

Specifically for Seifert 3-manifolds (such as lens spaces):

Review is in

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

See also:

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:

Relation to perturbative CS-observables

Relation to perturbative quantization of 3d Chern-Simons theory:

specifically to Reidemeister torsion:

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:

More in:

  • Jin-Beom Bae, Dongmin Gang, Jaehoon Lee, 3d 𝒩=2\mathcal{N}=2 minimal SCFTs from Wrapped M5-branes, JHEP 08 (2017) 118 (arXiv:1610.09259)

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 March 14, 2023 at 07:35:13. See the history of this page for a list of all contributions to it.