Unifying soft and hard dynamics: The hard current algebra in celestial holography

TL;DR

This paper introduces a unified algebraic framework combining soft and hard current algebras to describe both infrared and finite-energy scattering processes in flat spacetime, revealing new Ward identities.

Contribution

It uncovers an infinite-dimensional hard current algebra that encodes finite-energy effects and shows how soft algebras emerge from it, unifying the infrared and finite-energy descriptions.

Findings

Hard current algebra encodes finite-energy scattering contributions

Soft current algebras are derived from the hard algebra

New Ward identities relate soft and hard dynamics

Abstract

Soft current algebras capture the infrared structure of scattering in asymptotically flat spacetimes, but an analogous algebraic description of finite-energy dynamics has been missing. We uncover an infinite-dimensional hard current algebra that encodes finite-energy contributions to scattering and implies novel Ward identities. The soft current algebras are not independent but arise naturally from the hard ones. This provides a unified algebraic framework underlying quantum theory in flat spacetime.