Extended BMS Algebra of Celestial CFT

TL;DR

$T(z)$ is realized as the shadow transform of the soft graviton and generates superrotations in CCFT, while a dimension-2 descendant $P(z)$ encodes supertranslations; together, they realize the extended $rak{bms}_4$ algebra in celestial conformal field theory via OPEs derived from soft and collinear limits of Einstein–Yang–Mills theory. The authors show that the holomorphic Virasoro structure emerges from the $TT$ OPE with zero central charge, that $Tar T$ is regular, and that $T$ and $P$ mix in well-defined TP/OPEs, while all supertranslations can be packaged into a single primary ${ m P}(z,ar z)$ of dimension $( frac{3}{2}, frac{3}{2})$. They also provide a concrete construction of the full translation sector using a spectral-flow-like connection to the P generators, and outline how the CCFT framework could be extended to quantum corrections and spectrum analysis. The work relies on detailed collinear-limit analyses in EYM theory and uses conformal integrals to derive the required OPEs, offering a path toward a holographic description of 4D flat physics via CCFT at null infinity.

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.

Figures (3)

• Figure 1: Feynman diagrams leading to collinear graviton singularities.
• Figure 2: EYM Feynman diagrams leading to singularities for collinear gauge bosons and gravitons.
• Figure 3: EYM Feynman diagrams leading to gravitational corrections to Yang-Mills collinear singularities.