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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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.
|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.|
|Subject Keywords:||gauge theory; vortex equations; BPS invariants; D-branes; conformal field theory|
|Classification Code:||Mathematics Subject Classification (2000): 81T60, 81T30, 81T40, 14N35.|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Tony Diaz|
|Deposited On:||14 Dec 2011 16:33|
|Last Modified:||08 Mar 2013 22:09|
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