Asymptotic Symmetries in Electrodynamics and Kalb-Ramond Theory

TL;DR

This thesis investigates the asymptotic symmetries of the Kalb-Ramond field in four-dimensional spacetime, comparing different gauges and duality with scalar fields to understand their charges and fall-off conditions.

Contribution

It provides a detailed analysis of the asymptotic symmetries of the Kalb-Ramond field, including gauge-dependent charges and duality-based fall-off conditions, extending electrodynamics insights.

Findings

Radial gauge charge vanishes at infinity.

Kalb-Ramond and scalar field fall-off conditions are consistent.

Duality helps identify missing asymptotic symmetries.

Abstract

In this thesis, we aim to find the asymptotic symmetries of the Kalb-Ramond field in four dimensions at future null infinity. We start by reviewing the asymptotic symmetries of electrodynamics in four-dimensional Minkowski spacetime at future null infinity. We continue by investigating the asymptotic symmetries of the Kalb-Ramond field at future null infinity. We motivate the fall-off conditions by demanding the finiteness of energy, momentum, angular momentum and charge flux through future null infinity. We expand the gauge fields in ``radial" and Lorenz gauge and compute the generating charges. Using the duality between the Kalb-Ramond theory and the scalar field in two dimensions, we again derive the fields' fall-off conditions and compare them to the ones obtained above. Our findings can be summarized as follows: The different gauges yield two similar generating charges, however, the charge obtained in the ``radial" gauge vanishes at infinity. This result might indicate that the fall-off conditions are too strict in this gauge. We observe consistency in the asymptotic behaviours of Kalb-Ramond and scalar field theories. Even after we expanded both fields asymptotically, the fall-off conditions for the Kalb-Ramond field obtained by duality considerations are compatible with those derived from the finiteness conditions above. This might also allow us to address the question asked in \cite{Campiglia2018} about which are the missing asymptotic symmetries generated by the soft charges of scalar fields.