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 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.

Original languageEnglish
Article number149
JournalLetters in Mathematical Physics
Volume111
Issue number6
Early online date14 Dec 2021
DOIs
Publication statusPublished - Dec 2021

Keywords

  • BV formalism
  • fuzzy spaces
  • noncommutative field theory
  • triangular Hopf algebras

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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