Quantization of derived cotangent stacks and gauge theory on directed graphs

Benini, Marco; Pridham, Jonathan P.; Schenkel, Alexander

Abstract

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.

Citation

Benini, M., Pridham, J. P., & Schenkel, A. (2023). Quantization of derived cotangent stacks and gauge theory on directed graphs. Advances in Theoretical and Mathematical Physics, 27(5), 1275-1332. https://doi.org/10.4310/atmp.2023.v27.n5.a1

• Journal Article Type: Article
• Acceptance Date: Jul 20, 2023
• Online Publication Date: Jul 15, 2024
• Publication Date: 2023
• Deposit Date: Jul 18, 2024
• Publicly Available Date: Jul 18, 2024
• Journal: Advances in Theoretical and Mathematical Physics
• Print ISSN: 1095-0761
• Electronic ISSN: 1095-0753
• Publisher: International Press
• Peer Reviewed: Peer Reviewed
• Volume: 27
• Issue: 5
• Pages: 1275-1332
• DOI: https://doi.org/10.4310/atmp.2023.v27.n5.a1
• Public URL: https://nottingham-repository.worktribe.com/output/37312791
• Publisher URL: https://www.intlpress.com/site/pub/pages/journals/items/atmp/content/vols/0027/0005/a001/