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3-Manifolds and 3d indices

Dimofte, Tudor and Gaiotto, Davide and Gukov, Sergei (2013) 3-Manifolds and 3d indices. Advances in Theoretical and Mathematical Physics, 17 (5). pp. 975-1076. ISSN 1095-0761. doi:10.4310/ATMP.2013.v17.n5.a3.

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We identify a large class R of three-dimensional N = 2 superconformal field theories. This class includes the effective theories T_M of M5-branes wrapped on 3-manifolds M, discussed in previous work by the authors, and more generally comprises theories that admit a UV description as abelian Chern–Simons-matter theories with (possibly non-perturbative) superpotential. Mathematically, class R might be viewed as an extreme quantum generalization of the Bloch group; in particular, the equivalence relation among theories in class R is a quantum-field-theoretic “2 to 3 move.” We proceed to study the supersymmetric index of theories in class R, uncovering its physical and mathematical properties, including relations to algebras of line operators and to 4d indices. For 3-manifold theories T_M, the index is a new topological invariant, which turns out to be equivalent to non-holomorphic SL(2,ℂ) Chern–Simons theory on M with a previously unexplored “integration cycle.”

Item Type:Article
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URLURL TypeDescription Paper
Gukov, Sergei0000-0002-9486-1762
Additional Information:© 2013 International Press. We would like to thank Christopher Beem, Abhijit Gadde, Daniel Green, Anton Kapustin, Sara Pasquetti, Leonardo Rastelli, Schlomo Razamat, Nathan Seiberg, Cumrun Vafa, Roland van der Veen, and Edward Witten for illuminating discussions. The work of TD is supported primarily by the Friends of the Institute for Advanced Study, and in part by DOE grant DE-FG02-90ER40542. The work of DG is supported in part by NSF grant PHY-0503584 and in part by the Roger Dashen membership in the Institute for Advanced Study. The work of SG is supported in part by DOE Grant DE-FG03-92-ER40701 and in part by NSF Grant PHY-0757647. TD and SG thank the Simons Center for Geometry and Physics for their hospitality during the Simons Workshop in Mathematics and Physics, 2011, where part of this work was initiated. Opinions and conclusions expressed here are those of the authors and do not necessarily reflect the views of funding agencies.
Group:Caltech Theory
Funding AgencyGrant Number
Friends of the Institute for Advanced StudyUNSPECIFIED
Department of Energy (DOE)DE-FG02-90ER40542
Institute for Advanced StudyUNSPECIFIED
Department of Energy (DOE)DE-FG03-92-ER40701
Issue or Number:5
Record Number:CaltechAUTHORS:20140610-081020607
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:46170
Deposited By: Tony Diaz
Deposited On:10 Jun 2014 18:21
Last Modified:10 Nov 2021 17:21

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