Kähler流形上的Kapranov $L_\infty$结构、Fedosov星积和单圈精确BV量子化
Kapranov's $L_\infty$ structures, Fedosov's star products, and one-loop exact BV quantizations on Kähler manifolds
摘要：
我们研究了Kähler流形上的量子化方案，并涉及到几个有趣的结构。我们首先构造了Kähler流形$X$上的Fedosov星积作为Kapranov的$L_\infty$ -代数结构的量子化.然后我们研究了与这些星积相关的Batalin-Vilkovisky（BV）量子化。一个显着的特点是，它们都是单圈精确的，这意味着与两个或多个圈相关联的费曼权重都消失了。这导致了一个简洁的上链水平公式在德拉姆上同调的代数指数。
英文摘要：
We study quantization schemes on a Kähler manifold and relate several interesting structures. We first construct Fedosov's star products on a Kähler 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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