Kapranov's L-infinity structures, Fedosov's star products, and one-loop exact BV quantizations on Kahler manifolds

Chan Kwokwai; Leung Naichung Conan; Li Qin

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Kapranov's L-infinity structures, Fedosov's star products, and one-loop exact BV quantizations on Kahler manifolds

机译：Kapranov's L-infinity structures, Fedosov's star products, and one-loop exact BV quantizations on Kahler manifolds

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摘要

We study quantization schemes on a Kahler manifold and relate several interesting structures. We first construct Fedosov's star products on a Kahler manifold X as quantizations of Kapranov's L-infinity-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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《Communications in number theory and physics》 |2022年第2期|299-351|共53页
作者
Chan Kwokwai; Leung Naichung Conan; Li Qin;
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作者单位

Chinese Univ Hong Kong;

Southern Univ Sci & Technol;

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原文格式 PDF
正文语种英语
中图分类数学;
关键词
L-infinity structure; deformation quantization; BV quantization; algebraic index theorem; ROZANSKY-WITTEN INVARIANTS; TOEPLITZ QUANTIZATION; WICK TYPE; DEFORMATION; CONSTRUCTION; SEPARATION;

Kapranov's L-infinity structures, Fedosov's star products, and one-loop exact BV quantizations on Kahler manifolds

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