Edge observables in Maxwell theory on null boundaries

Abstract

We study edge observables in three-dimensional Maxwell theory on null boundaries using a Hamiltonian formulation adapted to null foliations. We consider three backgrounds: Minkowski spacetime, the BTZ black hole, and de Sitter space, where the relevant boundaries are, respectively, null infinity, the black hole horizon, and the cosmological horizon. In all three cases we find, besides the usual $U(1)$ charge, a second edge observable associated with an intrinsic symmetry on the null boundary. The two charges are well defined quasilocally. They form a centrally extended algebra which, in Fourier modes, becomes two independent Abelian Kac-Moody algebras with opposite levels. Thus, the same centrally extended edge structure appears at both asymptotic and finite-distance null boundaries.