Comments on holographic current algebras and asymptotically flat four dimensional spacetimes at null infinity

TL;DR

This work reframes charges and their algebras in four-dimensional asymptotically flat spacetimes at null infinity in terms of a holographic current algebra for the time component of currents, complemented by a complete spatial current algebra. It develops the classical theory for both global and gauge symmetries, then illustrates the framework with three-dimensional AdS$_3$ and flat examples, highlighting how current algebras arise from asymptotic symmetries and can feature central extensions. In four dimensions, it provides the solution space, transformation laws, and explicit time and spatial currents both without and with news, including non-integrable terms and field-dependent central extensions, and demonstrates how a local boundary formulation avoids divergences. The approach connects the Newman–Penrose variables with boundary current algebras and offers a covariant, contour-friendly route to the asymptotic charges on ${\mathcal I}^+$, unifying holographic current methods with the traditional BMS$_4$ structure.

Abstract

We follow the spirit of a recent proposal to show that previous computations for asymptotically flat spacetimes in four dimensions at null infinity can be re-interpreted in terms of a well-defined holographic current algebra for the time component of the currents. The analysis is completed by the current algebra for the spatial components.