Universal features of 2 →n scattering in QCD and gravity from shockwave collisions

A remarkable double-copy relation of Einstein gravity to QCD in Regge asymptotics is Γμν=12CμCν-12NμNν, where Γμν is the gravitational Lipatov vertex in the 2→3 graviton scattering amplitude, Cμ its Yang-Mills counterpart, and Nμ the QED bremsstrahlung vertex. In QCD, the Lipatov vertex is a fundamental building block of the BFKL equation describing the 2→N scattering of gluons at high energies. Likewise, the gravitational Lipatov vertex is a key ingredient in a 2D effective field theory framework describing trans-Planckian 2→N graviton scattering. We construct a quantitative correspondence between a semiclassical Yang-Mills framework for radiation in gluon shockwave collisions and its counterpart in general relativity. In particular, we demonstrate the Lipatov double copy in a dilute-dilute approximation corresponding to RS,L, RS,H b, where RS,L, RS,H are the respective emergent Schwarzchild radii generated in shockwave collisions and b is the impact parameter. We outline extensions of the correspondence developed here to the dilute-dense computation of gravitational wave radiation in the close vicinity of one of the black holes, the construction of graviton propagators in the shockwave background, and a renormalization group approach to compute 2→N amplitudes that incorporates graviton Reggeization and coherent graviton multiple scattering.