导出余切叠的量子化与有向图上的规范场论
Quantization of derived cotangent stacks and gauge theory on directed graphs
AI总结：
本文通过平展消解显式描述导出余切叠的泊松结构并量子化，进而构造出量子化有向图上规范场论的 dg-范畴值预因子化代数。
摘要：
我们研究了商叠的导出余切叠 $T^\ast[X/G]$ 上典型未平移泊松结构的量子化，其中 $X$ 是带有（约化）光滑仿射群概形 $G$ 作用的光滑仿射概形。这是通过使用叠状 CDGA 对 $T^\ast[X/G]$ 进行平展消解来实现的，该消解允许显式描述 $T^\ast[X/G]$ 上的典型泊松结构以及量子化它的模的 dg-范畴。这些技术被应用于构造一个取值于 dg-范畴的预因子化代数，该代数量子化了有向图上的规范场论。
英文摘要：
We study the quantization of the canonical unshifted Poisson structure on the derived cotangent stack $T^\ast[X/G]$ of a quotient stack, where $X$ is a smooth affine scheme with an action of a (reductive) smooth affine group scheme $G$. This is achieved through an {é}tale resolution of $T^\ast[X/G]$ by stacky CDGAs that allows for an explicit description of the canonical Poisson structure on $T^\ast[X/G]$ and of the dg-category of modules quantizing it. These techniques are applied to construct a dg-category-valued prefactorization algebra that quantizes a gauge theory on directed graphs.
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