BMS algebra as an extension of the Poincar\'e symmetry in light-cone gravity

TL;DR

This paper demonstrates that in light-cone gravity, the Poincaré symmetry can be locally extended to the BMS algebra without relying on asymptotic conditions, using a non-linear representation on physical degrees of freedom.

Contribution

It shows a local realization of BMS symmetry as an extension of Poincaré in four-dimensional light-cone gravity, avoiding asymptotic assumptions.

Findings

Poincaré algebra extended to BMS symmetry locally

Representation on helicity states with non-linear realization

No asymptotic limits needed for the extension

Abstract

We analyze possible local extensions of the Poincar\'e symmetry in light-cone gravity in four dimensions. We use a formalism where we represent the algebra on the two physical degrees of freedom, one with helicity $2$ and the other with helicity $-2$. The representation is non-linearly realized and one of the light-cone momenta is the Hamiltonian, which is hence a non-linear generator of the algebra. We find that this can be locally realized and the Poincar\'e algebra extended to the BMS symmetry without any reference to asymptotic limits.