On Double Gauging of U(1) Symmetry on Noncommutative Space

TL;DR

This paper explores a novel double gauging mechanism of U(1) symmetry on noncommutative space, revealing unique gauge interactions and field interpretations that differ from traditional approaches.

Contribution

It introduces a new framework for double gauging of U(1) symmetry on noncommutative space with distinct gauge interactions and field behavior.

Findings

Double gauging leads to new gauge field structures.

Interactions differ significantly from standard U(1) gauge theories.

In the commutative limit, gauge fields behave as expected.

Abstract

We point out that a field \phi charged under a global U(1) symmetry generally allows for a starred localized extension with the transformation rule, \phi\to U_L\star\phi\star U_R^{-1}. This results in a double gauging of the global U(1) symmetry on noncommutative space. We interpret the gauge theory so obtained in terms of the gauge fields that in the commutative limit appear naturally and are respectively the gauge field responsible for the charge and a decoupled vector field. The interactions are shown to be very different from those obtained by assigning a transformation rule of \phi\to U\star\phi or \phi\star U^{-1}.