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

Chan，Kwokwai1; Leung，Naichung Conan2; Li，Qin3

2022

10.4310/CNTP.2022.v16.n2.a2

Communications in Number Theory and Physics   影响因子和分区

1931-4523

1931-4531

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-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.

Algebraic index theorem Bv quantization Deformation quantization L∞ structure

英语

其他

National Natural Science Foundation of China[12071204];

2-s2.0-85130388738

Scopus

1.Department of Mathematics,The Chinese University of Hong Kong,Shatin,Hong Kong,Hong Kong
2.The Institute of Mathematical Sciences and Department of Mathematics,The Chinese University of Hong Kong,Shatin,Hong Kong,Hong Kong
3.Shenzhen Institute for Quantum Science and Engineering,Southern University of Science and Technology,Shenzhen,China

Chan，Kwokwai,Leung，Naichung Conan,Li，Qin. Kapranov’s L∞ structures, Fedosov’s star products, and one-loop exact BV quantizations on Kahler manifolds[J]. Communications in Number Theory and Physics,2022,16(2):299-351.

Chan，Kwokwai,Leung，Naichung Conan,&Li，Qin.(2022).Kapranov’s L∞ structures, Fedosov’s star products, and one-loop exact BV quantizations on Kahler manifolds.Communications in Number Theory and Physics,16(2),299-351.

Chan，Kwokwai,et al."Kapranov’s L∞ structures, Fedosov’s star products, and one-loop exact BV quantizations on Kahler manifolds".Communications in Number Theory and Physics 16.2(2022):299-351.