Celestial holography on Kerr-Schild backgrounds

Abstract

We explore the celestial holography proposal for non-trivial asymptotically flat backgrounds including the Coulomb field of a static and spinning point charge, their gravitational counterparts described by the Schwarzschild and Kerr metrics, as well as the Aichelburg-Sexl shockwave and spinning shockwave geometries and their electromagnetic cousins. We compute celestial two-point amplitudes on these Kerr-Schild type backgrounds which have the desirable feature, due to the presence of an external source, that they are non-vanishing for general operator positions and are not constrained by the kinematic delta functions of flat space celestial CFT correlators. Of particular interest is the case of shockwave backgrounds where the two-point scattering amplitude of massless scalars can be interpreted as a standard CFT three-point correlator between two massless asymptotic states and a conformal primary shockwave operator. We furthermore show that the boundary on-shell action for general backgrounds becomes the generating functional for tree-level correlation functions in celestial CFT. Finally, we derive (conformal) Faddeev-Kulish dressings for particle-like backgrounds which remove all infrared divergent terms in the two-point functions to all orders in perturbation theory.

The ultrarelativistic limit of Kerr

“…For the BN amplitude (4.8), the UV is regulated and the transform can converge in some range of parameters (away from the poles). A similar effect was also observed by [58] for probe scattering in the Ferrari-Pendenza metric, where the source has infinite size in the transverse plane.…”

“…While it is not appropriate to describe the massless limit of the Kerr metric, it is worth noting that the metric (3.15) still has some interesting applications. For instance, in celestial holography it corresponds to a conformal primary operator on the celestial sphere [57], and celestial amplitudes computed in this background have surprisingly good convergence properties [58] -probably due to the extended nature of the source (3.17).…”

Self-Dual Black Holes in Celestial Holography

“…The most pressing one may be the computation of higher-point (n ≥ 2 points) correlation functions of graviton operators from our state |M, a . In fact, an interesting computation of conformal two-point functions in Kerr backgrounds has been presented recently in [71]. We devote the rest of this section to showing that those results are consistent with our state.…”

“…19 Connections between black holes and 4D Wilson line insertions in the S-matrix have resurfaced recently in the context of gravitational effective field theories and the binary black hole problem, see e.g. [52,53,55,71,112,113].…”

“…We conclude with a discussion in Section 6. Appendices A and B include more details about classical Kleinian metrics and operators on the celestial torus, respectively, and Appendix C presents a connection of our work to the recent four-point amplitudes calculations in [71].…”