Superboost transitions, refraction memory and super-Lorentz charge algebra

TL;DR

This paper characterizes the space of Minkowski vacua under super-Lorentz transformations, linking impulsive transitions to gravitational memory effects and establishing a phase space with a rich asymptotic symmetry group consistent with soft graviton theorems.

Contribution

It provides a closed-form description of Minkowski vacua under arbitrary Diff(S^2) transformations and introduces a phase space with a renormalized symplectic structure aligned with soft graviton theorems.

Findings

Derived explicit orbit of Minkowski spacetime under super-Lorentz transformations.

Linked impulsive transitions to refraction and displacement memory effects.

Established a phase space with a symmetry group matching soft graviton theorems.

Abstract

We derive a closed-form expression of the orbit of Minkowski spacetime under arbitrary Diff$(S^2)$ super-Lorentz transformations and supertranslations. Such vacua are labelled by the superboost, superrotation and supertranslation fields. Impulsive transitions among vacua are related to the refraction memory effect and the displacement memory effect. A phase space is defined whose asymptotic symmetry group consists of arbitrary Diff$(S^2)$ super-Lorentz transformations and supertranslations. It requires a renormalization of the symplectic structure. We show that our final surface charge expressions are consistent with the leading and subleading soft graviton theorems. We contrast the leading BMS triangle structure to the mixed overleading/subleading BMS square structure.