Revisiting the Symmetries of Galilean Electrodynamics

TL;DR

This paper analyzes the symmetries of various Galilean electrodynamics theories, correcting previous results and revealing their infinite-dimensional nature, with implications for non-relativistic holography.

Contribution

It corrects and extends the understanding of symmetries in Galilean electrodynamics, showing they are always infinite-dimensional and identifying their algebraic structure.

Findings

Symmetries of GED are infinite-dimensional in all dimensions.

In 3+1 dimensions, symmetries form the conformal Milne algebra extended by a spatial dilatation.

Results have implications for non-relativistic AdS/CFT correspondence.

Abstract

We determine the symmetries of four different theories: I) Galilean Electrodynamics (GED), II) GED coupled to 5 free static scalar fields, III) Galilean Yang-Mills (GYM), and IV) GYM coupled to 5 interacting scalar fields. We correct some old results in the literature, by finding that the symmetries of GED in a spacetime of generic dimension $d+1$ is always infinite dimensional, and in $3+1$ they correspond to the conformal Milne algebra extended by a spatial dilatation generator, which we call $D_x$. Finally, we comment on how these results fit into the framework of the non-relativistic AdS$_5$/CFT$_4$ correspondence.