Non-minimal couplings to $U(1)$-gauge fields and asymptotic symmetries

TL;DR

This paper investigates the asymptotic symmetries of electromagnetism with non-minimal scalar couplings, showing that these couplings do not alter the asymptotic symmetry structure compared to the free theory, and analyzing the effects of duality and gauge transformations.

Contribution

It demonstrates that non-minimal scalar couplings in electromagnetism do not change the asymptotic symmetry group, extending understanding of gauge symmetries in extended supergravity models.

Findings

Asymptotic symmetries remain the same as the free theory with non-minimal couplings.

Duality symmetry is broken to a compact subgroup by asymptotic conditions.

Logarithmic gauge transformations help simplify the symmetry algebra.

Abstract

We analyse the asymptotic symmetries of electromagnetism non-minimally coupled to scalar fields, with non-minimal couplings of the Fermi type that occur in extended supergravity models. Our study is carried out at spatial infinity where minimal and non-minimal couplings exhibit very different asymptotic properties: while the former generically cannot be neglected at infinity, the latter can. Electromagnetic non-minimal couplings are in that respect similar to gravitational minimal couplings, which are also asymptotically subdominant. Because the non-minimally interacting model is asymptotic to the free one, its asymptotic symmetries are the same as the ones of the free theory, i.e., described by angle-dependent $u(1)$ gauge transformations. We also analyse the duality symmetry and show that it is broken to its compact subgroup by the asymptotic conditions. Finally, we consider logarithmic gauge transformations and use them to simplify the symmetry algebra.