Batalin-Vilkovisky quantization of fuzzy field theories

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.

v4: Final version accepted for publication in Letters in Mathematical Physics

References in corpus (2)

• Statistics and UV-IR Mixing with Twisted Poincare Invariance
• Lectures on shifted Poisson geometry

Cited by in corpus (3)

• Braided $L_{\infty }$-Algebras, Braided Field Theory and Noncommutative Gravity
• Braided Symmetries in Noncommutative Field Theory
• On multimatrix models motivated by random noncommutative geometry II: A Yang-Mills-Higgs matrix model