Chiral Bosons in Noncommutative Spacetime

TL;DR

This paper develops a Lorentz covariant chiral boson model in a (1+1)-dimensional noncommutative spacetime, revealing that noncommutativity blurs the distinction between left- and right-moving modes and affects the system's self-duality.

Contribution

It introduces a novel noncommutative chiral boson Lagrangian with manifest Lorentz covariance and explores its unique properties, including the indistinguishability of chiral modes and the application of Dirac's method.

Findings

Left- and right-moving chiral scalars are indistinguishable due to noncommutativity.

Dirac's method is applicable to the constrained noncommutative system.

The noncommutative chiral boson action lacks self-duality.

Abstract

Underlying a general noncommutative algebra with both noncommutative coordinates and noncommutative momenta in a (1+1)-dimensional spacetime, a chiral boson Lagrangian with manifest Lorentz covariance is proposed by linearly imposing a generalized self-duality condition on a noncommutative generalization of massless real scalar fields. A significant property uncovered for noncommutative chiral bosons is that the left- and right-moving chiral scalars cannot be distinguished from each other, which originates from the noncommutativity of coordinates and momenta. An interesting result is that Dirac's method can be consistently applied to the constrained system whose Lagrangian explicitly contains space and time. The self-duality of the noncommutative chiral boson action does not exist.