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 ∗ [ 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 ´etale resolution of T ∗ [ X/G ] by stacky CDGAs that allows for an explicit description of the canonical Poisson structure on T ∗ [ 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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