Topics on the Quantum Dynamics of Chiral Bosons

TL;DR

This paper explores various formulations of chiral bosons, analyzing their relationships using canonical methods, and reveals the duality and symmetry properties, including the role of the noton in quantum dynamics and anomalies.

Contribution

It demonstrates the duality between Siegel and Floreanini-Jackiw models without gauge-fixing, highlighting the noton's role in symmetry and quantum anomalies.

Findings

Discloses the presence of a noton in different formulations.

Establishes the duality between Siegel and Floreanini-Jackiw models.

Shows the noton carries symmetry content and influences anomalies.

Abstract

Chiral bosons are important building blocks in the study of supergravity, string theory and quantum Hall effect. Along the last two decades many different formulations have appeared trying to describe the dynamics and the quantization of these curious objects. However two of them have gain special attention among people working on this area: the gauge invariant formulation proposed by Siegel and the noninvariant one put forward by Floreanini and Jackiw. We call these distinct analysis as chiral bosonization schemes (CBS). In this report we make a study of the relationships among many of these different chiral bosonization schemes. This is done in the context canonical framework with two different techniques known as soldering formalism and dual projection formalism. The first considers the phenomenon of interference between chiral modes and the second is able to separate dynamics from the symmetry behavior in a quantum field theory. While the soldering formalism discloses phenomena analogous to the double slit interference phenomena in classical-quantum physics with important consequences to the bosonization program, the dual projection, in particular, is able to disclose the presence of a noton, a nonmover field, in different formulations for chiral bosons. The importance of this last result is that it proves the duality between Siegel and Floreanini-Jackiw model without invoking gauge-fixing: while the Floreanini-Jackiw component describes the dynamics, it is the noton that carries the symmetry contents, acquiring dynamics upon quantization and is fully responsible for the Siegel anomaly.