Gukov, Sergei and Pei, Du and Putrov, Pavel and Vafa, Cumrun
(2017)
*BPS spectra and 3-manifold invariants.*
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(Submitted)
https://resolver.caltech.edu/CaltechAUTHORS:20170201-100930550

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## Abstract

We provide a physical definition of new homological invariants H_a(M_3) of 3-manifolds (possibly, with knots) labeled by abelian flat connections. The physical system in question involves a 6d fivebrane theory on M3 times a 2-disk, D^2, whose Hilbert space of BPS states plays the role of a basic building block in categorification of various partition functions of 3d N = 2 theory T[M3]: D^2 × S^1 half-index, S^2 × S^1 superconformal index, and S^2 × S^1 topologically twisted index. The first partition function is labeled by a choice of boundary condition and provides a refinement of Chern-Simons (WRT) invariant. A linear combination of them in the unrefined limit gives the analytically continued WRT invariant of M_3. The last two can be factorized into the product of half-indices. We show how this works explicitly for many examples, including Lens spaces, circle fibrations over Riemann surfaces, and plumbed 3-manifolds

Item Type: | Report or Paper (Discussion Paper) | ||||||||||||||
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Additional Information: | Submitted 23 January 2017. We would like to thank J. E. Andersen, M. Aganagic, F. Benini, C. Cordova, A. Gadde, E. Gorsky, K. Hori, H. Kim, S. Nawata, M. Romo, S. Shakirov, L. Rozansky and K. Ye for useful comments and discussions. The work of S.G. and D.P. is supported in part by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632. In addition, the work of D.P. is supported by the center of excellence grant “Center for Quantum Geometry of Moduli Space” from the Danish National Research Foundation (DNRF95). P.P. gratefully acknowledges the support from Marvin L. Goldberger Fellowship and the DOE Grant DE-SC0009988. The research of C.V. is supported in part by NSF grant PHY-1067976. This work was performed in part (by P.P.) at Aspen Center for Physics which is supported by National Science Foundation grant PHY-1066293. The authors would like to thank Simons Center for Geometry and Physics and the organisers of the Simons Summer Workshop 2016, where the work on the project has begun, for generous hospitality. | ||||||||||||||

Group: | Walter Burke Institute for Theoretical Physics | ||||||||||||||

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Record Number: | CaltechAUTHORS:20170201-100930550 | ||||||||||||||

Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20170201-100930550 | ||||||||||||||

Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||||

ID Code: | 73923 | ||||||||||||||

Collection: | CaltechAUTHORS | ||||||||||||||

Deposited By: | Joy Painter | ||||||||||||||

Deposited On: | 01 Feb 2017 19:48 | ||||||||||||||

Last Modified: | 03 Oct 2019 16:32 |

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