Extended BMS Algebra of Celestial CFT

TL;DR

This paper explores the extended BMS algebra in celestial CFT, deriving operator product expansions and demonstrating how supertranslations and superrotations are represented within the framework of flat holography.

Contribution

It provides a detailed derivation of OPEs for BMS operators and clarifies the role of soft gravitons in generating supertranslations and superrotations in celestial CFT.

Findings

Derived OPEs for BMS superrotation and supertranslation operators.

Showed superrotations form a Virasoro subalgebra in celestial CFT.

Unified supertranslations into a single primary conformal operator.

Abstract

We elaborate on the proposal of flat holography in which four-dimensional physics is encoded in two-dimensional celestial conformal field theory (CCFT). The symmetry underlying CCFT is the extended BMS symmetry of (asymptotically) flat spacetime. We use soft and collinear theorems of Einstein-Yang-Mills theory to derive the OPEs of BMS field operators generating superrotations and supertranslations. The energy-momentum tensor, given by a shadow transform of a soft graviton operator, implements superrotations in the Virasoro subalgebra of $\mathfrak{bms_4}$. Supertranslations can be obtained from a single translation generator along the light-cone direction by commuting it with the energy-momentum tensor. This operator also originates from a soft graviton and generates a flow of conformal dimensions. All supertranslations can be assembled into a single primary conformal field operator on celestial sphere.