Supertranslation-invariant dressed Lorentz charges

Abstract

We present an explicit formula for Lorentz boosts and rotations that commute with BMS supertranslations in asymptotically flat spacetimes. Key to the construction is the use of infrared regularizations and of a unitary transformation that makes observables commute with the soft degrees of freedom. We explicitly verify that our charges satisfy the Lorentz algebra and we check that they are consistent with expectations by evaluating them on the supertranslated Minkowski space and on the boosted Kerr black hole.

Logarithmic supertranslations and supertranslation-invariant Lorentz charges

“…Once this is done, the pure supertranslations and the logarithmic supertranslations have vanishing Poisson brackets with all the Poincaré generators. The decoupling of the pure supertranslations agrees with the ideas pursued in [22][23][24][25] along different quantum lines. In particular, there are some similarities between the logarithmic supertranslation charges and the boundary gravitons of [24,25] which are conjugate to the supertranslations in that work.…”

“…The decoupling of the pure supertranslations agrees with the ideas pursued in [22][23][24][25] along different quantum lines. In particular, there are some similarities between the logarithmic supertranslation charges and the boundary gravitons of [24,25] which are conjugate to the supertranslations in that work. Our considerations are, however, purely classical, do not need any form of regularization, and fulfill automatically all necessary Jacobi identity required by consistency since we work with a well-defined Poisson bracket.…”

“…The new Poincaré generators are invariant under supertranslations. As we have pointed out, this decoupling is conceptually very similar to the decoupling achieved in [22][23][24][25], but our approach is entirely classical (non-quantum). The decoupling amounts to add to the Lorentz transformations appropriately chosen supertranslations and logarithmic supertranslations with coefficients that depend on the charges.…”

“…• Since our new boundary conditions allow logarithmic supertranslations, a natural question is: what are the Ward identities associated with these new symmetries [45][46][47]? Furthermore, in view of the decoupling mechanism, one might wonder whether these Ward identities would provide new insightful information on "hard processes", or merely constraint "soft processes", see [22][23][24][25].…”

Asymptotic $$ \mathcal{O} $$(r) gauge symmetries and gauge-invariant Poincaré generators in higher spacetime dimensions

“…Now, it is precisely the presence of these central charges which allowed, through a suitable nonlinear redefinition of the Lorentz generators, to disentangle the whole set of pure supertranslations (standard and logarithmic ones) from the Lorentz algebra, finding in this manner a resolution to the angular momentum ambiguity under supertranslations at spatial infinity. Note that different mechanisms have been developed at null infinity [9][10][11][12] (see also [13][14][15] and references therein).…”