Chern-Simons-Rozansky-Witten topological field theory
Apr, 2009Citations per year
Abstract: (Elsevier)
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 .Note:
- 31 pages, latex, typo on page 18 corrected
- field theory: topological
- space: affine
- dimension: 3
- supersymmetry: algebra
- supersymmetry: twist
- space-time: Kaehler
- Chern-Simons term
- gauge field theory
- Wilson loop
- category
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