Duality and Braiding in Twisted Quantum Field Theory

TL;DR

This paper clarifies the properties of twisted quantum field theories on noncommutative spaces, showing their equivalence to commutative theories, and explores their behavior under dualities and background magnetic fields.

Contribution

It introduces a nonlocal field redefinition framework and braided tensor algebra techniques to better understand twisted quantum field theories and their dualities.

Findings

Green's functions are formally equivalent in noncommutative and commutative theories

Twisted Fock space states obey conventional statistics

Background magnetic fields induce additional twists and alter noncommutative geometry

Abstract

We re-examine various issues surrounding the definition of twisted quantum field theories on flat noncommutative spaces. We propose an interpretation based on nonlocal commutative field redefinitions which clarifies previously observed properties such as the formal equivalence of Green's functions in the noncommutative and commutative theories, causality, and the absence of UV/IR mixing. We use these fields to define the functional integral formulation of twisted quantum field theory. We exploit techniques from braided tensor algebra to argue that the twisted Fock space states of these free fields obey conventional statistics. We support our claims with a detailed analysis of the modifications induced in the presence of background magnetic fields, which induces additional twists by magnetic translation operators and alters the effective noncommutative geometry seen by the twisted quantum fields. When two such field theories are dual to one another, we demonstrate that only our braided physical states are covariant under the duality.