Simplifying (super-)BMS algebras

TL;DR

This paper demonstrates that certain non-linear asymptotic symmetry algebras in higher-dimensional gravity and supergravity can be redefined into a direct sum structure, clarifying their commutation relations and charge properties.

Contribution

The authors show how to redefine non-linear BMS and super-BMS algebras into a direct sum form, simplifying their structure and understanding of asymptotic symmetries.

Findings

Reformulation of BMS$_5$ and super-BMS$_4$ algebras into direct sums.

Angle-dependent translations and supersymmetries commute with Poincaré generators in the new form.

Detailed analysis of charge-integrability for field-dependent symmetry parameters.

Abstract

We show that the non-linear BMS$_5$ symmetry algebra of asymptotically flat Einstein gravity in five dimensions, as well as the super-BMS$_4$ superalgebra of asymptotically flat supergravity, can be redefined so as to take a direct sum structure. In the new presentation of the (super-)algebra, angle-dependent translations and angle-dependent supersymmetry transformations commute with the (super-)Poincar\'e generators. We also explain in detail the structure and charge-integrability of asymptotic symmetries with symmetry parameters depending on the fields (through the charges themselves), a topic relevant for nonlinear asymptotic symmetry algebras.