Asymptotic Symmetries in Electrodynamics and Kalb-Ramond Theory

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 theradial" 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.