Microscopic unitary description of tidal excitations in high-energy string-brane collisions

Abstract

The eikonal operator was originally introduced to describe the effect of tidal excitations on higher-genus elastic string amplitudes at high energy. In this paper we provide a precise interpretation for this operator through the explicit tree-level calculation of generic inelastic transitions between closed strings as they scatter off a stack of parallel Dp-branes. We perform this analysis both in the light-cone gauge, using the Green-Schwarz vertex, and in the covariant formalism, using the Reggeon vertex operator. We also present a detailed discussion of the high-energy behaviour of the covariant string amplitudes, showing how to take into account the energy factors that enhance the contribution of the longitudinally polarized massive states in a simple way.

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

“…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. In [5,6] (see also [8,9]) the microscopic structure of this S-matrix was analyzed in much detail.…”

“…For this reason in this section we will derive, following the discussion in ref. [5], a general formula for the imaginary part of the elastic scattering amplitude of an arbitrary closed string off the Dp-branes in the Regge limit.…”

“…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.…”

“…Elastic and inelastic amplitudes for arbitrary states of the string spectrum become more and more complex as the number of possible contractions between momenta and polarizations increases. Their structure however drastically simplifies in the Regge limit and, as discussed in [5], it is possible to give a general and explicit formula in terms of the matrix elements of the phase of the eikonal operator [4,11,12]. The Regge limit is characterized by a single spatial direction of large momentum that naturally leads to a separation of the dynamics in a longitudinal and a transverse part.…”

“…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.…”