Celestial sector in CFT: Conformally soft symmetries

Abstract

We show that time intervals of width \Delta \tauΔτ in 3-dimensional conformal field theories (CFT_33) on the Lorentzian cylinder admit an infinite dimensional symmetry enhancement in the limit \Delta \tau → 0Δτ→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_44 algebra. We analyze the shadow stress tensor Ward identities in CFT_dd on the Lorentzian cylinder with all operator insertions in infinitesimal time intervals separated by \piπ. We demonstrate that both the leading and subleading conformally soft graviton theorems in (d-1)(d−1)-dimensional celestial CFT (CCFT_{d-1}d−1) can be recovered from the transverse traceless components of these Ward identities in the limit \Delta \tau → 0Δτ→0. A similar construction allows for the leading conformally soft gluon theorem in CCFT_{d-1}d−1 to be recovered from shadow current Ward identities in CFT_dd.