Fivebranes and 3-manifold homology
By Sergei Gukov, Pavel Putrov, C. Vafa. 2016
168 citations recorded by the source corpus.
A bstractMotivated by physical constructions of homological knot invariants, we study their analogs for closed 3-manifolds. We show that fivebrane compactifications provide a universal description of various old and new homological invariants of 3-manifolds. In terms of 3d/3d correspondence, such invariants are given by the Q-cohomology of the Hilbert space of partially topologically twisted 3d N=2$$ \mathcal{N}=2 $$ theory T[M3] on a Riemann surface with defects. We demonstrate this by concrete and explicit calculations in the case of monopole/Heegaard Floer homology and a 3-manifold analog of Khovanov-Rozansky link homology. The latter gives a categorification of Chern-Simons partition function. Some of the new key elements include the explicit form of the S-transform and a novel connection between categorification and a previously mysterious role of Eichler integrals in Chern-Simons theory.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/aa275073a62375cad4f64d21e6954dd319771b1c
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Citations in the corpus
- BPS spectra and 3-manifold invariants (2017, methodology): “ is only one homological block Zb 0(q;t), realized as the S1 D2 partition function of the Nfree chirals with Neumann boundary conditions, Zb 0(q;t) = YN i=1 1 (tiqi;q) 1 : (3.3) In the terminology of [27] this is an unreduced homological block.26 In order to relate it to the WRT invariant of S3 as i”
- Comments on twisted indices in 3d supersymmetric gauge theories (2016, background): “2 N = 2 theories on Σg have also been studied recently in [20, 21].”