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Equivariant Verlinde formula from fivebranes and vortices

Gukov, Sergei and Pei, Du (2017) Equivariant Verlinde formula from fivebranes and vortices. Communications in Mathematical Physics, 355 (1). pp. 1-50. ISSN 0010-3616. doi:10.1007/s00220-017-2931-9.

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We study complex Chern–Simons theory on a Seifert manifold M_3 by embedding it into string theory. We show that complex Chern–Simons theory on M_3 is equivalent to a topologically twisted supersymmetric theory and its partition function can be naturally regularized by turning on a mass parameter. We find that the dimensional reduction of this theory to 2d gives the low energy dynamics of vortices in four-dimensional gauge theory, the fact apparently overlooked in the vortex literature. We also generalize the relations between (1) the Verlinde algebra, (2) quantum cohomology of the Grassmannian, (3) Chern–Simons theory on Σ×S^1 and (4) index of a spin^c Dirac operator on the moduli space of flat connections to a new set of relations between (1) the “equivariant Verlinde algebra” for a complex group, (2) the equivariant quantum K-theory of the vortex moduli space, (3) complex Chern–Simons theory on Σ×S^1 and (4) the equivariant index of a spin^c Dirac operator on the moduli space of Higgs bundles.

Item Type:Article
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URLURL TypeDescription ReadCube access Paper
Gukov, Sergei0000-0002-9486-1762
Pei, Du0000-0001-5587-6905
Additional Information:© 2017 Springer-Verlag GmbH Germany. Received: 02 June 2016; Accepted: 03 May 2017; First Online: 03 July 2017. We wish to thank Anton Alekseev for a wonderful set of notes [67] that we recommend to all the beginners. We also thank S. Shatashvili for discussions of this work in Fall 2013 and Spring 2014, which stimulated [60].We also benefited from discussions with Mina Aganagic, Sir Michael Atiyah, Tudor Dimofte, Abhijit Gadde, Jaume Gomis, Nigel Hitchin, Tadashi Okazaki, Satoshi Okuda, Pavel Putrov, Richard Wentworth and Wenbin Yan. This work is funded by the DOE Grant DE-SC0011632, NSF Grants DMS 1107452, 1107263, 1107367 (the GEAR Network), and the Walter Burke Institute for Theoretical Physics.
Group:Walter Burke Institute for Theoretical Physics
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Department of Energy (DOE)DE-SC0011632
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
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Issue or Number:1
Record Number:CaltechAUTHORS:20150220-093858198
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Official Citation:Gukov, S. & Pei, D. Commun. Math. Phys. (2017) 355: 1.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:55045
Deposited By: Joy Painter
Deposited On:20 Feb 2015 17:59
Last Modified:10 Nov 2021 20:40

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