BMS charge algebra

Abstract

ABSTRACT. The surface charges associated with the symmetries of asymptotically flat four dimensional spacetimes at null infinity are constructed. They realize the symmetry algebra in general only up to a field-dependent central extension that satisfies a suitably generalized cocycle condition. This extension vanishes when using the globally well defined BMS algebra. For the Kerr black hole and the enlarged BMS algebra with both supertranslations and superrotations, some of the supertranslations charges diverge whereas there are no divergences for the superrotation charges. The central extension is proportional to the rotation parameter and involves divergent integrals on the sphere.

Flat holography: aspects of the dual field theory

“…In [59], the authors concluded that the only non-trivial central terms that the algebra could have are the Virasoro central extensions to the Witt algebra of the first line. In [60], the same set of authors concluded that the Virasoro central terms were 2 This section was worked out in collaboration with Anandita De. 3 Here it is of interest to mention that the BMS4 group has also been recently extended differently to include all smooth vector fields on S 2 instead of extending the global conformal symmetries to Virasoro symmetries [57,58].…”

On soft theorems and form factors in N = 4 $$ \mathcal{N}=4 $$ SYM theory

“…Recent progress in the study of soft behavior of scattering amplitudes was made within the context of BMS [6,7] and extended BMS [8][9][10][11] asymptotic symmetries for asymptotically Minkowskian spacetimes. BMS and extended BMS transformations are infinitesimal diffeomorphisms, which preserve a prescribed structure of spacetime at future or past null infinities I ± , but act nontrivially on the physical data residing there.…”

“…The solution of the eigenvalue equation 10 for monodromy matrix eq. (5.6) leads to the expressions for Yangian invariants labeled by the permutations σ with minimal 11 decomposition σ = (i P , j P ) .…”

On higher-spin supertranslations and superrotations

“…[9][10][11][12][13][14][15]), and soft theorems, i.e. relations among scattering amplitudes for processes involving the emission or the absorption of low-energy particles [2,3].…”