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arXiv · 1302.3227

A Topological Chern-Simons Sigma Model and New Invariants of Three-Manifolds

Yuan Luo·Meng-Chwan Tan
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Abstract

We construct a topological Chern-Simons sigma model on a Riemannian three-manifold M with gauge group G whose hyperkahler target space X is equipped with a G-action. Via a perturbative computation of its partition function, we obtain new topological invariants of M that define new weight systems which are characterized by both Lie algebra structure and hyperkahler geometry. In canonically quantizing the sigma model, we find that the partition function on certain M can be expressed in terms of Chern-Simons knot invariants of M and the intersection number of certain G-equivariant cycles in the moduli space of G-covariant maps from M to X. We also construct supersymmetric Wilson loop operators, and via a perturbative computation of their expectation value, we obtain new knot invariants of M that define new knot weight systems which are also characterized by both Lie algebra structure and hyperkahler geometry.

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Yuan Luo, Meng-Chwan Tan. 2014-01-23. A Topological Chern-Simons Sigma Model and New Invariants of Three-Manifolds. https://doi.org/10.1007/jhep02(2014)067

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