第一类复量子陈-西蒙斯理论

IF 0.6 3区数学 Q3 MATHEMATICS

Journal of Symplectic Geometry Pub Date : 2020-12-31 DOI:10.4310/JSG.2022.v20.n6.a1

J. Andersen, A. Malusà, Gabriele Rembado

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引用次数: 3

摘要

研究了闭属1曲面和半单复群的Chern—Simons理论的几何量子化问题。首先，我们引入了K\ {a}hler量化中Hitchin连接的自然复化模拟，其极化来自平坦连接的模空间的非阿贝尔Hodge超K\ {a}hler几何，从而补充了Witten的实极化方法。然后考虑Witten连接，并利用模空间上极化截面上的Bargmann变换的一个版本，将其与复化的Hitchin连接进行了标识。

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Genus-one complex quantum Chern–Simons theory

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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来源期刊

Journal of Symplectic Geometry 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Publishes high quality papers on all aspects of symplectic geometry, with its deep roots in mathematics, going back to Huygens’ study of optics and to the Hamilton Jacobi formulation of mechanics. Nearly all branches of mathematics are treated, including many parts of dynamical systems, representation theory, combinatorics, packing problems, algebraic geometry, and differential topology.