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Gauge Theories Labelled by Three-Manifolds

Dimofte, Tudor and Gaiotto, Davide and Gukov, Sergei (2014) Gauge Theories Labelled by Three-Manifolds. Communications in Mathematical Physics, 325 (2). pp. 367-419. ISSN 0010-3616. doi:10.1007/s00220-013-1863-2.

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We propose a dictionary between geometry of triangulated 3-manifolds and physics of three-dimensional N=2 gauge theories. Under this duality, standard operations on triangulated 3-manifolds and various invariants thereof (classical as well as quantum) find a natural interpretation in field theory. For example, independence of the SL(2) Chern-Simons partition function on the choice of triangulation translates to a statement that S^3_b partition functions of two mirror 3d N=2 gauge theories are equal. Three-dimensional N=2 field theories associated to 3-manifolds can be thought of as theories that describe boundary conditions and duality walls in four-dimensional N=2 SCFTs, thus making the whole construction functorial with respect to cobordisms and gluing.

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Gukov, Sergei0000-0002-9486-1762
Additional Information:© 2013 Springer-Verlag Berlin Heidelberg. Received: 15 May 2012. Accepted: 6 July 2013. Published online: 15 December 2013. We wish to thank A. Kapustin, N. Seiberg, C. Vafa, R. van der Veen, and E. Witten for many helpful and enlightening discussions. The work of TD is supported in part by NSF Grant PHY-0969448. 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 Kavli Institute for Theoretical Physics (research supported by DARPA under Grant No. HR0011-09-1-0015 and by the National Science Foundation under Grant No. PHY05-51164 and the Simons Center for Geometry and Physics for their hospitality in the summer of 2011. TD also acknowledges the Max Planck Institut für Mathematik for its hospitality and support during June, 2011. Opinions and conclusions expressed here are those of the authors and do not necessarily reflect the views of funding agencies. Communicated by N. A. Nekrasov
Group:Caltech Theory
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Institute for Advanced StudyUNSPECIFIED
Department of Energy (DOE)DE-FG03-92-ER40701
Defense Advanced Research Projects Agency (DARPA)HR0011-09-1-0015
Simons Center for Geometry and PhysicsUNSPECIFIED
Max Planck Institut für MathematikUNSPECIFIED
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Issue or Number:2
Record Number:CaltechAUTHORS:20140210-154717900
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ID Code:43760
Deposited By: Ruth Sustaita
Deposited On:11 Feb 2014 15:56
Last Modified:10 Nov 2021 16:42

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