Twisted Yang–Mills field theory: connections and Noether currents

Abstract

Main properties of noncommutative (NC) gauge theory are investigated in a two-dimensional twisted Moyal plane, generated by vector fields Xa = eμ a (x)∂μ; the dynamical effects are induced by a nontrivial tensor eμ a (x). Connections in such a NC space are defined. Symmetry analysis is performed and related NC action is proved to be invariant under defined NC gauge transformations. A locally conserved Noether current is explicitly computed. Both commuting and noncommutative vector fields Xa are considered.