Memory Correlators and Ward Identities in the 'in-in' Formalism

TL;DR

This paper explores the role of Ward identities and memory correlators in the 'in-in' formalism for asymptotically flat spacetimes, linking soft graviton insertions to celestial CFT observations.

Contribution

It derives Ward identities for supertranslations within the 'in-in' formalism and connects memory correlators to celestial CFT observables, extending the understanding of asymptotic symmetries.

Findings

Connected memory correlators are non-trivial in the 'in-in' formalism.

Soft charge two-point functions can be computed explicitly.

Memory correlators relate to average null energy (ANEC) correlators.

Abstract

The symmetries of asymptotically flat spacetimes impose constraints on observables at infinity. The consequences of this have been extensively explored for S-matrix elements, where soft theorems are known to be equivalent to Ward identities for asymptotic symmetries. However, recently there has been interest in broader classes of asymptotic observables. Here, we consider soft graviton insertions in the 'in-in' formalism. We derive a Ward identity for supertranslations and compute two point functions for the soft charges for 'in-in' correlators. We find that the connected memory correlators are non-trivial in this set up and can be straightforwardly inferred from the average null energy (ANEC) correlators using observations from celestial Conformal Field Theory (cCFT).