Quantization of derived cotangent stacks and gauge theory on directed graphs

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 étale 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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The work of M.B. is fostered by the National Group of Mathematical Physics (GNFM-INdAM (IT)).

A.S. gratefully acknowledges the financial support of the Royal Society (UK) through a Royal Society University Research Fellowship (URF\R\211015) and the Enhancement Awards (RGF\EA\180270, RGF\EA\201051 and RF\ERE\210053).

Published 15 July 2024