Batalin–Vilkovisky quantization of fuzzy field theories

Nguyen, Hans; Schenkel, Alexander; Szabo, Richard J.

Abstract

We apply the modern Batalin–Vilkovisky quantization techniques of Costello and Gwilliam to noncommutative field theories in the finite-dimensional case of fuzzy spaces. We further develop a generalization of this framework to theories that are equivariant under a triangular Hopf algebra symmetry, which in particular leads to quantizations of finite-dimensional analogues of the field theories proposed recently through the notion of ‘braided L∞-algebras’. The techniques are illustrated by computing perturbative correlation functions for scalar and Chern–Simons theories on the fuzzy 2-sphere, as well as for braided scalar field theories on the fuzzy 2-torus.

Citation

Nguyen, H., Schenkel, A., & Szabo, R. J. (2021). Batalin–Vilkovisky quantization of fuzzy field theories. Letters in Mathematical Physics, 111(6), Article 149. https://doi.org/10.1007/s11005-021-01490-2

• Journal Article Type: Article
• Acceptance Date: Nov 18, 2021
• Online Publication Date: Dec 14, 2021
• Publication Date: Dec 1, 2021
• Deposit Date: Dec 16, 2021
• Publicly Available Date: Dec 16, 2021
• Journal: Letters in Mathematical Physics
• Print ISSN: 0377-9017
• Electronic ISSN: 1573-0530
• Publisher: Springer Science and Business Media LLC
• Peer Reviewed: Peer Reviewed
• Volume: 111
• Issue: 6
• Article Number: 149
• DOI: https://doi.org/10.1007/s11005-021-01490-2
• Keywords: Mathematical Physics; Statistical and Nonlinear Physics
• Public URL: https://nottingham-repository.worktribe.com/output/7020064
• Publisher URL: https://link.springer.com/article/10.1007/s11005-021-01490-2