Superboost transitions, refraction memory and super-Lorentz charge algebra

Abstract

We derive a closed-form expression of the orbit of Minkowski spacetime under arbitrary DiffpS 2 q 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 DiffpS 2 q 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. 1

Asymptotic Symmetries in the Gauge fixing Approach and the BMS group

“…These equations can be readily solved and the solutions are given by where Diff(S 2 ) are the smooth superrotations generated by Y A and S are the smooth supertranslations generated by T . This extension of the original global BMS 4 algebra (see below) is called the generalized BMS 4 algebra [67][68][69][70]. Therefore, the Λ-BMS 4 algebra reduces in the flat limit to the smooth extension (3.69) of the BMS 4 algebra.…”

“…• The non-integrability of the charges may be circumvented by different procedures to isolate an integrable part in the expression of the charges (see e.g. [95] and [69]). However, the final integrated surface charges obtained by these procedures do not have all the properties that integrable charges would have.…”

“…Another philosophy is to keep working with non-integrable expressions, without making any specific choice for the integrable part of the charges. In some situations, it is still possible to define a modified bracket for the charges, leading to a representation of the asymptotic symmetry algebra, up to a 2-cocycle which may depend on fields [69,90]. However, no general representation theorem exists in this context, even if some progress has been made [96].…”

“…As mentioned above, the infinitesimal surface charges are not integrable. Therefore, we cannot unambiguously define an integrated surface charge as in (4.53) (see, however, [69,95]). In particular, the representation theorem (4.54) does not hold.…”

“…This triangle controlling the infrared structure of the theory has also been constructed for other gauge theories [148,166,167]. Furthermore, subleading infrared triangles have been uncovered and discussed [69,166,[168][169][170][171]. In particular, the Ward identities of superrotations have been shown to be equivalent to the subleading soft graviton theorem.…”