Twisted Yang-Mills field theory: connections and Noether current

TL;DR

This paper explores the properties of noncommutative gauge theory on a twisted 2D Moyal plane, defining connections, analyzing symmetries, and deriving a conserved Noether current, with implications for NC field theories.

Contribution

It introduces a framework for connections and gauge invariance in a twisted noncommutative space, including explicit computation of a conserved Noether current.

Findings

Gauge invariance of the NC action is established.

A conserved Noether current is explicitly derived.

Both commuting and noncommuting vector fields are considered.

Abstract

Main properties of noncommutative (NC) gauge theory are investigated in a $2-$dimensional twisted Moyal plane, generated by vector fields $X_{a}=e_{a}^{\mu}(x)\partial_{\mu};$ the dynamical effects are induced by a non trivial tensor $e_{a}^{\mu}(x)$. 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 $X_{a}$ are considered.