Celestial ${\mathrm{CFT}}_d$ with symmetry group $\mathrm{ISO}(d+1,1)$ is the putative dual of quantum gravity in asymptotically flat ($d+2$) dimensional space time. We argue that a class of $d$ dimensional field theories with symmetry group $\mathrm{ISO}(d+1,1)$, refereed to as Poincaré ${\mathrm{CFT}}_d$, can be engineered via ${\mathrm{AdS}}_{d+1}\text{−}{\mathrm{CFT}}_d$ correspondence. Celestial and Poincaré ${\mathrm{CFT}}_d$ may share common features determined by the kinematics because they have the same symmetry group. So understanding Poincaré CFTs may help us better understand some features of celestial CFTs. Our argument is based on the observation that if we zoom in near the boundary of (Euclidean) ${\mathrm{AdS}}_{d+1}$ then the conformal isometry group of ${\mathrm{EAdS}}_{d+1}$, which is $\mathrm{SO}(d+2,1)$, contracts to the Poincaré group $\mathrm{ISO}(d+1,1)$. This suggests that the near boundary scaling limit of a theory of conformal gravity on ${\mathrm{EAdS}}_{d+1}$ should be dual to a boundary ${\mathrm{CFT}}_d$ with $\mathrm{ISO}(d+1,1)$ symmetry. This dual ${\mathrm{CFT}}_d$ is an example of a Poincaré ${\mathrm{CFT}}_d$. Similarly, if we have a nonconformal theory of gravity on ${\mathrm{EAdS}}_{d+1}$ then the near boundary scaling limit of such a theory is dual to a Poincaré ${\mathrm{CFT}}_d$ with only [$\mathrm{SO}(d+1,1)$] Lorentz invariance. This class of less symmetric Poincaré ${\mathrm{CFT}}_d$ is analogous to celestial ${\mathrm{CFT}}_d$ which computes the leaf amplitudes. Now following this logic we discuss, among other things, the near boundary scaling limit of the bosonic string theory on Euclidean ${\mathrm{AdS}}_3$ in the presence of the NS-NS B field. The ${\mathrm{AdS}}_3$ part of the world sheet theory is free in this limit and has been studied in the literature in different contexts. This limit describes a “long string” which wraps the (Euclidean) ${\mathrm{AdS}}_3$ boundary and it has been argued that the space-time ${\mathrm{CFT}}_2$ which describes the radial fluctuations of a long string is a Liouville CFT. According to our proposal, the dual ${\mathrm{CFT}}_2$ which describes the long string sector is an example of a Poincaré ${\mathrm{CFT}}_2$ with only [SO(3,1)] Lorentz invariance. We do not get a full ISO(3,1) invariant Poincaré ${\mathrm{CFT}}_2$ in this way because the string theory does not have target space conformal invariance.

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• Gauge-gravity dualities
• Quantum gravity
• Strings & branes