On the Mathai-Quillen Formalism of Topological Sigma Models

Details On the Mathai-Quillen Formalism of Topological Sigma Models On the Mathai-Quillen Formalism of Topological Sigma Models

1994-06-15

arxiv.org/abs/hep-th/9406103v1

J.Geom.Phys. 17 (1995) 299-309

Physics

High Energy Physics

High Energy Physics - Theory

12 pages, plain LaTeX

Scientific paper

10.1016/0393-0440(94)00046-8

We present a Mathai-Quillen interpretation of topological sigma models. The key to the construction is a natural connection in a suitable infinite dimensional vector bundle over the space of maps from a Riemann surface (the world sheet) to an almost complex manifold (the target). We show that the covariant derivative of the section defined by the differential operator that appears in the equation for pseudo-holomorphic curves is precisely the linearization of the operator itself. We also discuss the Mathai-Quillen formalism of gauged topological sigma models.

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