Chiral sound waves from a gauge theory of 1D generalized statistics

TL;DR

This paper introduces a 1D topological gauge theory with two U(1) Kaeld-Moody algebras that results in chiral bosonic sound waves, similar to Luttinger liquid density fluctuations.

Contribution

It develops a novel gauge-theoretic framework for 1D systems that produces chiral sound waves, extending concepts from higher-dimensional topological field theories.

Findings

Sound waves are chiral bosonic excitations.

Spectrum matches Luttinger model density fluctuations.

Gauge coupling induces statistical transmutation.

Abstract

A topological gauge field theory in one spatial dimension is studied, with the gauge fields as generators of two commuting U(1) Ka\u{c}-Moody algebras. Coupling of these gauge fields to nonrelativistic bosonic matter fields, produces a statistical transmutation of the later, as in the Chern-Simons theory in two dimensions. The sound waves of the model are investigated and proven to be chiral bosonic excitations, with the same spectrum as the density fluctuations of the Luttinger model.