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arXiv · 2012.15630

Genus-one complex quantum Chern--Simons theory

Jørgen Ellegaard Andersen·Alessandro Malusà·Gabriele Rembado
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Abstract

We consider the geometric quantisation of Chern--Simons theory for closed genus-one surfaces and semisimple complex groups. First we introduce the natural complexified analogue of the Hitchin connection in K\"{a}hler quantisation, with polarisations coming from the nonabelian Hodge hyper-K\"{a}hler geometry of the moduli spaces of flat connections, thereby complementing the real-polarised approach of Witten. Then we consider the connection of Witten, and we identify it with the complexified Hitchin connection using a version of the Bargmann transform on polarised sections over the moduli spaces.

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Jørgen Ellegaard Andersen, Alessandro Malusà, Gabriele Rembado. 2020-12-31. Genus-one complex quantum Chern--Simons theory. https://doi.org/10.4310/jsg.2022.v20.n6.a1

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