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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. https://resolver.caltech.edu/CaltechAUTHORS:20150220-093858198

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Abstract

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
Related URLs:
URLURL TypeDescription
https://dx.doi.org/10.1007/s00220-017-2931-9DOIArticle
https://link.springer.com/article/10.1007%2Fs00220-017-2931-9PublisherArticle
http://rdcu.be/tZb3PublisherFree ReadCube access
http://arxiv.org/abs/1501.01310arXivDiscussion Paper
ORCID:
AuthorORCID
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
Funders:
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0011632
NSFDMS-1107452
NSFDMS-107263
NSFDMS-1107367
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Other Numbering System:
Other Numbering System NameOther Numbering System ID
CALT-TH2014-171
Issue or Number:1
Record Number:CaltechAUTHORS:20150220-093858198
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20150220-093858198
Official Citation:Gukov, S. & Pei, D. Commun. Math. Phys. (2017) 355: 1. https://doi.org/10.1007/s00220-017-2931-9
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:55045
Collection:CaltechAUTHORS
Deposited By: Joy Painter
Deposited On:20 Feb 2015 17:59
Last Modified:03 Oct 2019 08:02

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