High-energy string-brane scattering: leading eikonal and beyond

Abstract

We extend previous techniques for calculations of transplanckian-energy stringstring collisions to the high-energy scattering of massless closed strings from a stack of N Dp-branes in Minkowski spacetime. We show that an effective non-trivial metric emerges from the string scattering amplitudes by comparing them against the semiclassical dynamics of high-energy strings in the extremal p-brane background. By changing the energy, impact parameter and effective open string coupling λ = gN , we are able to explore various interesting regimes and to reproduce classical expectations, including tidal-force excitations, even beyond the leading-eikonal approximation.

A microscopic description of absorption in high-energy string-brane collisions

“…There is also a string-size-corrected weak-gravity regime (corresponding to somewhat smaller impact parameters) in which tidal excitations of the incoming closed string become important or even dominant [4]. In this regime we are still able to provide an exactly unitary S-matrix, but unitarity now works in an enlarged Hilbert space containing excited closed strings besides the incoming one.…”

“…It can be simplified, however, under the assumption that R p , while comparable or even larger than b, is still smaller than the string length parameter l s , enhanced by a square root of the logarithm of the energy, as we will discuss in more detail in the rest of the paper. 1 When this is the case the eikonal resummation of the leading terms (in energy) of the higher-order string amplitudes [4,11,12] should give a correct representation of the dynamics for every value of the impact parameter, all the way down to b = 0. Although in this limit a geometric interpretation of the brane background is lacking, the dynamics of the string-brane system remains extremely rich and interesting.…”

“…Then, in order to obtain a formula for the total splitting probability valid for an arbitrary closed string state, we will review the results of ref. [5], where it is shown that a simple and efficient way to calculate the Regge limit of a generic elastic (or inelastic) closed-closed scattering amplitude is to evaluate the matrix elements of the eikonal operator for string-brane scattering [4]. As particular cases 2 The disk amplitudes for an arbitrary number of open and closed strings with Neumann boundary conditions were first computed in ref.…”

“…In a series of relatively recent papers [4][5][6][7] we have addressed the problem of the highenergy collision of a closed string off a configuration of parallel Dp-branes. By suitably playing with the various parameters characterizing the process, the number N of branes, the energy E and impact parameter b of the collision, as well as the string coupling g s , we could identify [4] a region in parameter space inside which closed string loops can be safely neglected and, consequently, there is no closed string production or gravitational bremsstrahlung, a considerable simplification.…”

“…By suitably playing with the various parameters characterizing the process, the number N of branes, the energy E and impact parameter b of the collision, as well as the string coupling g s , we could identify [4] a region in parameter space inside which closed string loops can be safely neglected and, consequently, there is no closed string production or gravitational bremsstrahlung, a considerable simplification. Even within this region there are several interesting regimes to study.…”