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Vortex Counting and Lagrangian 3-Manifolds

Dimofte, Tudor and Gukov, Sergei and Hollands, Lotte (2011) Vortex Counting and Lagrangian 3-Manifolds. Letters in Mathematical Physics, 98 (3). pp. 225-287. ISSN 0377-9017 . http://resolver.caltech.edu/CaltechAUTHORS:20111209-105547167

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Abstract

To every 3-manifold M one can associate a two-dimensional N=(2,2) supersymmetric field theory by compactifying five-dimensional N=2 super-Yang–Mills theory on M. This system naturally appears in the study of half-BPS surface operators in four-dimensional N=2 gauge theories on one hand, and in the geometric approach to knot homologies, on the other. We study the relation between vortex counting in such two-dimensional N=(2,2) supersymmetric field theories and the refined BPS invariants of the dual geometries. In certain cases, this counting can also be mapped to the computation of degenerate conformal blocks in two-dimensional CFT’s. Degenerate limits of vertex operators in CFT receive a simple interpretation via geometric transitions in BPS counting.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1007/s11005-011-0531-8DOIArticle
http://www.springerlink.com/content/t4j13462k5672297/PublisherArticle
http://arxiv.org/abs/1006.0977arXivDiscussion Paper
Additional Information:© 2011 Springer. Received: 3 March 2011; Revised: 30 August 2011; Accepted: 9 September 2011. Published online: 5 October 2011. We would like to thank M. Aganagic, C. Beem, A. Borodin, A. Braverman, A. Gorsky, C. Keller, H. Nakajima, J. Song, and E. Witten for very useful discussions, and C. Vafa for collaboration at an earlier stage of this project. The work of SG and LH is supported in part by NSF grant PHY-0757647. The work of SG is also supported in part by DOE grant DE-FG03-92-ER40701 and in part by the Alfred P. Sloan Foundation. Opinions and conclusions expressed here are those of the authors and do not necessarily reflect the views of funding agencies.
Group:Caltech Theory
Funders:
Funding AgencyGrant Number
NSFPHY-0757647
Department of Energy (DOE)DE-FG03-92-ER40701
Alfred P. Sloan FoundationUNSPECIFIED
Subject Keywords:gauge theory; vortex equations; BPS invariants; D-branes; conformal field theory
Classification Code:Mathematics Subject Classification (2000): 81T60, 81T30, 81T40, 14N35.
Record Number:CaltechAUTHORS:20111209-105547167
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20111209-105547167
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:28396
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:14 Dec 2011 16:33
Last Modified:23 Aug 2016 10:08

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