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Chern–Simons–Rozansky–Witten topological field theory

Kapustin, Anton and Saulina, Natalia (2009) Chern–Simons–Rozansky–Witten topological field theory. Nuclear Physics B, 823 (3). pp. 403-427. ISSN 0550-3213.

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We construct and study a new topological field theory in three dimensions. It is a hybrid between Chern–Simons and Rozansky–Witten theory and can be regarded as a topologically-twisted version of the N=4 d=3 supersymmetric gauge theory recently discovered by Gaiotto and Witten. The model depends on a gauge group G and a hyper-Kähler manifold X with a tri-holomorphic action of G. In the case when X is an affine space, we show that the model is equivalent to Chern–Simons theory whose gauge group is a supergroup. This explains the role of Lie superalgebras in the construction of Gaiotto and Witten. For general X, our model appears to be new. We describe some of its properties, focusing on the case when G is simple and X is the cotangent bundle of the flag variety of G. In particular, we show that Wilson loops are labeled by objects of a certain category which is a quantum deformation of the equivariant derived category of coherent sheaves on X.

Item Type:Article
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URLURL TypeDescription Paper
Kapustin, Anton0000-0003-3903-5158
Additional Information:© 2009 Elsevier B.V. Received 11 May 2009; accepted 1 July 2009. Available online 8 July 2009. A.K. would like to thank Lev Rozansky and Sergey Arkhipov for valuable discussions. This work was supported in part by the DOE grant DE-FG03-92-ER40701.
Funding AgencyGrant Number
Department of Energy (DOE)DE-FG03-92-ER40701
Issue or Number:3
Record Number:CaltechAUTHORS:20091103-111212673
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Official Citation:Anton Kapustin, Natalia Saulina, Chern-Simons-Rozansky-Witten topological field theory, Nuclear Physics B, Volume 823, Issue 3, 21 December 2009, Pages 403-427, ISSN 0550-3213, DOI: 10.1016/j.nuclphysb.2009.07.006.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:16558
Deposited By: Tony Diaz
Deposited On:04 Nov 2009 22:08
Last Modified:03 Oct 2019 01:13

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