A remarkable double copy relation of Einstein gravity to QCD in Regge asymptotics is Γμν=12CμCν12NμNν, where Γμν is the gravitational Lipatov vertex in the 23 graviton scattering amplitude, Cμ its Yang-Mills counterpart, and Nμ the QED bremssstrahlung vertex. In QCD, the Lipatov vertex is a fundamental building block of the BFKL equation describing 2N scattering of gluons at high energies. Likewise, the gravitational Lipatov vertex is a key ingredient in a 2-D effective field theory framework describing trans-Planckian 2N graviton scattering. We construct a quantitative correspondence between a semi-classical 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, with RS,L, RS,H 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 close vicinity of one of the black holes, the construction of graviton propagators in the shockwave background, and a renormalization group approach to compute 2N amplitudes that incorporates graviton reggeization and coherent graviton multiple scattering.

H. Raj, R. Venugopalan, “Universal features of 2N scattering in QCD and gravity from shockwave
collisions”, Nov. 6, 2023, arXiv:2311.03463 (2023).


Related to Project C05, Co6