Rescattering corrections and self-consistent metric in planckian scattering

Abstract

Starting from the ACV approach to transplanckian scattering, we present a development of the reduced-action model in which the (improved) eikonal representation is able to describe particles' motion at large scattering angle and, furthermore, UV-safe (regular) rescattering solutions are found and incorporated in the metric. The resulting particles' shock-waves undergo calculable trajectory shifts and time delays during the scattering process -which turns out to be consistently described by both action and metric, up to relative order R 2 /b 2 in the gravitational radius over impact parameter expansion. Some suggestions about the role and the (re)scattering properties of irregular solutionsnot fully investigated here -are also presented.

Bulk phase shift, CFT Regge limit and Einstein gravity

“…More precisely, the four points on the boundary are Point 1 : 5 Notice that this statement does not assume bulk locality. The fact that τ = 0 is the first instance when excitations can interact follows from boundary causality [31].…”

“…A useful way to chart distinct physical regimes in a gravitational theory is to study scattering as a function of energy S and impact parameter L [1][2][3], see also figure 1 in [4]. In flat space the relevant quantity, namely the phase shift δ(S, L), is related to the Fourier transform of the four-point scattering amplitude A(s, t = − q 2 ) with respect to the transferred momentum q, see also [5,6]. In AdS the phase shift is given by the convolution of the four-point function of local operators with proper external wave functions [7][8][9][10][11].…”

Radiation enhancement and ``temperature'' in the collapse regime of gravitational scattering

“…This structure, which is valid for large impact parameters, i.e., for small values of the ratio R=b ≪ 1, provides a unitary S-matrix describing the Einstein deflection of the scattered particles as well as its associated graviton radiation and its metric fields [9,26] and time delays [27]. Actually, the subject of this paper is to extend the above picture to smaller impact parameters b ∼ R where the gravitational interaction becomes really strong and a gravitational collapse is expected on classical grounds.…”

Unitarity restoring graviton radiation in the collapse regime of gravitational scattering

“…Finally, the basic question comes back: what about the collapse regime of b < b c , in which the energy 2E appears to be "trapped" because elastic unitarity is exponentially violated by the suppression factors (1.4) without apparent contributions in the most naive radiation models [8,16,26,27]? In other words, is unsuppressed radiation predictable for b < b c in our present soft-based representation?…”

“…Starting from that leading eikonal approximation, the strategy followed in [6,7] consisted in a systematic study of subleading corrections to the eikonal phase, scattering angle, and time delays [8][9][10] in terms of the expansion parameter R 2 =b 2 (and possibly l 2 s =b 2 if working within string theory at scale l s ). These corrections can be resummed, in principle, by solving a classical field theory and one can thus study the critical region b ∼ R where gravitational collapse is expected.…”