Massless Scalars and Higher-Spin BMS in Any Dimension

TL;DR

This paper extends the BMS group to higher-spin symmetries in any dimension using massless scalar fields, proposing a new algebraic structure as the asymptotic symmetry of a hypothetical higher-spin gravity theory.

Contribution

It introduces two higher-spin extensions of the BMS group based on massless scalar fields, connecting Carrollian geometry to asymptotic symmetries in any dimension.

Findings

Constructed higher-spin BMS extensions with conformal properties.

Related BMS representations to scalar massless Poincare representations.

Proposed higher-spin algebra as asymptotic symmetry of exotic gravity theory.

Abstract

Starting from the asymptotic kinematics of massless scalar fields near null infinity in any spacetime dimension, we build two higher-spin extensions of the Carrollian definition of the BMS group and its generalisations. The first extension exhibits conformal properties reminiscent of the singleton in Anti-de Sitter space. The second acts on the space of radiative solutions of the d'Alembert equation, i.e. on Sachs's representation of BMS, which we relate to the scalar massless Poincare representation and extend to any Carrollian manifold. The corresponding enveloping algebra is a higher-spin extension of BMS that can be interpreted as the asymptotic symmetry of a putative exotic higher-spin gravity theory around Minkowski spacetime. Along the way, we provide a pedagogical introduction to Carrollian geometry and its relation to BMS.