Abstract
AbstractWe 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 $$L_\infty $$
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.
Funder
royal society
science and technology facilities council
Publisher
Springer Science and Business Media LLC
Subject
Mathematical Physics,Statistical and Nonlinear Physics
Cited by
5 articles.
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