Celestial Sector in CFT: Conformally Soft Symmetries

TL;DR

This paper reveals an infinite-dimensional symmetry enhancement in 3D conformal field theories on the Lorentzian cylinder as time intervals shrink, connecting these symmetries to celestial holography and soft theorems.

Contribution

It introduces a novel symmetry enhancement in CFT$_3$ related to the extended BMS$_4$ algebra and links shadow stress tensor Ward identities to soft graviton and gluon theorems in celestial CFT.

Findings

Infinite-dimensional symmetry enhancement in CFT$_3$ as $ au$ interval shrinks.

Recovery of soft graviton theorems from Ward identities in CFT$_d$.

Derivation of soft gluon theorems from shadow current Ward identities.

Abstract

We show that time intervals of width $\Delta \tau$ in 3-dimensional conformal field theories (CFT$_3$) on the Lorentzian cylinder admit an infinite dimensional symmetry enhancement in the limit $\Delta \tau \rightarrow 0$. The associated vector fields are approximate solutions to the conformal Killing equations in the strip labelled by a function and a conformal Killing vector on the sphere. An Inonu-Wigner contraction yields a set of symmetry generators obeying the extended BMS$_4$ algebra. We analyze the shadow stress tensor Ward identities in CFT$_d$ on the Lorentzian cylinder with all operator insertions in infinitesimal time intervals separated by $\pi$. We demonstrate that both the leading and subleading conformally soft graviton theorems in $(d-1)$-dimensional celestial CFT (CCFT$_{d-1}$) can be recovered from the transverse traceless components of these Ward identities in the limit $\Delta \tau \rightarrow 0$. A similar construction allows for the leading conformally soft gluon theorem in CCFT$_{d-1}$ to be recovered from shadow current Ward identities in CFT$_d$.