Vortex Counting and Lagrangian 3-Manifolds
- Creators
- Dimofte, Tudor
-
Gukov, Sergei
- Hollands, Lotte
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.
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.Attached Files
Submitted - 1006.0977v1.pdf
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Additional details
- Eprint ID
- 28396
- Resolver ID
- CaltechAUTHORS:20111209-105547167
- NSF
- PHY-0757647
- Department of Energy (DOE)
- DE-FG03-92-ER40701
- Alfred P. Sloan Foundation
- Created
-
2011-12-14Created from EPrint's datestamp field
- Updated
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2021-11-09Created from EPrint's last_modified field
- Caltech groups
- Caltech Theory