Celestial sector in CFT: Conformally soft symmetries

We show that time intervals of width Δτ in 3-dimensional conformal field theories (CFT ₃ 3) on the Lorentzian cylinder admit an infinite dimensional symmetry enhancement in the limit → 0 Δτ→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 4 algebra. We analyze the shadow stress tensor Ward identities in CFT d d on the Lorentzian cylinder with all operator insertions in infinitesimal time intervals separated by π. We demonstrate that both the leading and subleading conformally soft graviton theorems in (d-1) (d−1) -dimensional celestial CFT (CCFT ₃-₁ d−1) can be recovered from the transverse traceless components of these Ward identities in the limit → 0 Δτ→0. A similar construction allows for the leading conformally soft gluon theorem in CCFT ₃-₁ d−1 to be recovered from shadow current Ward identities in CFT d d.