Batalin–Vilkovisky quantization of fuzzy field theories
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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.
2017 ◽
Vol 20
(K2)
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pp. 107-116
2021 ◽
Vol 2090
(1)
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pp. 012067
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2014 ◽
Vol 66
(4)
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pp. 1375-1385
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1977 ◽
Vol 28
(1)
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pp. 116-117
2015 ◽
Vol 168
(2)
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pp. 441-445
2004 ◽
Vol 2
(3)
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pp. 253-265
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