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Published April 2016 | Submitted + Published
Journal Article Open

3d-3d Correspondence Revisited


In fivebrane compactifications on 3-manifolds, we point out the importance of all flat connections in the proper definition of the effective 3d 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.

Additional Information

© 2016 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Article funded by SCOAP3. Received: March 4, 2016; Accepted: April 13, 2016; Published: April 21, 2016. We would like to thank S. Nawata, S. Razamat, B. Willett, and E. Witten for useful discussions. Many ideas in this paper were developed at the 2013 Simons Summer Workshop in Mathematics and Physics, whose support and hospitality we gratefully acknowledge. The work of H.J.C. and S.G. is supported in part by DOE Grant DE-FG02-92ER40701. The work of T.D. is supported in part by DOE grant DE-SC0009988. This work has also been supported by the ERC Starting Grant no. 335739 "Quantum fields and knot homologies", funded by the European Research Council under the European Union's Seventh Framework Programme.

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Published - art_3A10.1007_2FJHEP04_282016_29140.pdf

Submitted - 1405.3663.pdf


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