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arXiv · 2008.07057

Kapranov's $L_\infty$ structures, Fedosov's star products, and one-loop exact BV quantizations on K\"ahler manifolds

Kwokwai Chan·Naichung Conan Leung·Qin Li
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Abstract

We study quantization schemes on a K\"ahler manifold and relate several interesting structures. We first construct Fedosov's star products on a K\"ahler manifold $X$ as quantizations of Kapranov's $L_\infty$-algebra structure. Then we investigate the Batalin-Vilkovisky (BV) quantizations associated to these star products. A remarkable feature is that they are all one-loop exact, meaning that the Feynman weights associated to graphs with two or more loops all vanish. This leads to a succinct cochain level formula in de Rham cohomology for the algebraic index.

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Kwokwai Chan, Naichung Conan Leung, Qin Li. 2020-08-17. Kapranov's $L_\infty$ structures, Fedosov's star products, and one-loop exact BV quantizations on K\"ahler manifolds. https://doi.org/10.4310/cntp.2022.v16.n2.a2

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