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arXiv · 2107.02532

Batalin-Vilkovisky quantization of fuzzy field theories

Hans Nguyen·Alexander Schenkel·Richard J. Szabo
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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 analogs of the field theories proposed recently through the notion of `braided $L_\infty$-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.

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BibTeXRIS

Hans Nguyen, Alexander Schenkel, Richard J. Szabo. 2021-07-06. Batalin-Vilkovisky quantization of fuzzy field theories. https://doi.org/10.1007/s11005-021-01490-2

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