Batalin–Vilkovisky quantization of fuzzy field theories

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, wh...

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Bibliographic Details
Published in:Letters in mathematical physics 2021-12, Vol.111 (6), Article 149
Main Authors: Nguyen, Hans, Schenkel, Alexander, Szabo, Richard J.
Format: Article
Language:English
Subjects:
Braiding
Complex Systems
Field theory (physics)
Geometry
Group Theory and Generalizations
Mathematical and Computational Physics
Measurement
Physics
Physics and Astronomy
Quantum theory
Scalars
Theoretical
Toruses
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Summary: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.
ISSN:0377-9017
1573-0530
DOI:10.1007/s11005-021-01490-2