Celestial sector in CFT: Conformally soft symmetries

Pipolo de Gioia, Leonardo; Raclariu, Ana Maria

doi:10.21468/SciPostPhys.17.1.002

SciPost Physics

Celestial sector in CFT: Conformally soft symmetries

Leonardo Pipolo de Gioia, Ana-Maria Raclariu

SciPost Phys. 17, 002 (2024) · published 2 July 2024

doi: 10.21468/SciPostPhys.17.1.002
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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 $\Delta \tau → 0$ . 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 $\Delta \tau → 0$ . 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 $_d$ .

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.17.1.002
TI  - Celestial sector in CFT: Conformally soft symmetries
PY  - 2024/07/02
UR  - https://scipost.org/SciPostPhys.17.1.002
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 17
IS  - 1
SP  - 002
A1  - Pipolo de Gioia, Leonardo
AU  - Raclariu, Ana Maria
AB  - 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 $\Delta \tau → 0$. 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 $\Delta \tau → 0$. 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$_d$.
ER  -

@Article{10.21468/SciPostPhys.17.1.002,
	title={{Celestial sector in CFT: Conformally soft symmetries}},
	author={Leonardo Pipolo de Gioia and Ana-Maria Raclariu},
	journal={SciPost Phys.},
	volume={17},
	pages={002},
	year={2024},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.17.1.002},
	url={https://scipost.org/10.21468/SciPostPhys.17.1.002},
}

Cited by 3

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¹ Leonardo Pipolo de Gioia,
² Ana Maria Raclariu

Funders for the research work leading to this publication