Galilean Conformal Electrodynamics

TL;DR

This work identifies infinite-dimensional Galilean conformal symmetry as the underlying structure of Galilean electrodynamics in both the Electric and Magnetic non-relativistic limits, realized in D=4 through intrinsic GCFT analysis and contraction from relativistic Maxwell theory. It introduces scale-spin primaries and two dynamical labels a and b that are fixed by the dynamics, yielding a genuinely non-relativistic conformal field theory in D>2. The authors also show a GCFT in D=3 via a dual scalar formulation and discuss correlation functions, holographic connections, and future extensions to Yang–Mills and supersymmetry. The results open avenues for non-relativistic holography, integrable sectors, and flat-space dualities within a well-defined GCFT framework.

Abstract

Maxwell's Electrodynamics admits two distinct Galilean limits called the Electric and Magnetic limits. We show that the equations of motion in both these limits are invariant under the Galilean Conformal Algebra in D=4, thereby exhibiting non-relativistic conformal symmetries. Remarkably, the symmetries are infinite dimensional and thus Galilean Electrodynamics give us the first example of an infinitely extended Galilean Conformal Field Theory in D>2. We examine details of the theory by looking at purely non-relativistic conformal methods and also use input from the limit of the relativistic theory.