Quantization of derived cotangent stacks and gauge theory on directed graphs

Abstract

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.

v3: 38 pages. Final version accepted for publication in Advances in Theoretical and Mathematical Physics