Topological Chern-Simons Sigma Model

Details Topological Chern-Simons Sigma Model Topological Chern-Simons Sigma Model

2009-07-09

arxiv.org/abs/0907.1641v2

JHEP 0909:122,2009

Physics

High Energy Physics

High Energy Physics - Theory

31 pages, no figure; v2. references added

Scientific paper

10.1088/1126-6708/2009/09/122

We consider topological twisting of recently constructed Chern-Simons-matter theories in three dimensions with N=4 or higher supersymmetry. We enumerate physically inequivalent twistings for each N, and find two different twistings for N=4, one for N=5,6, and four for N=8. We construct the two types of N=4 topological theories, which we call A/B-models, in full detail. The A-model has been recently studied by Kapustin and Saulina. The B-model is new and it consists solely of a Chern-Simons term of a complex gauge field up to BRST-exact terms. We also compare the new theories with topological Yang-Mills theories and find some interesting connections. In particular, the A-model seems to offer a new perspective on Casson invariant and its relation to Rozansky-Witten theory.

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