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

TL;DR

This work provides a microscopic, unitary description of tidal excitations in high-energy string-brane collisions by formulating the leading eikonal phase as an operator acting on the string’s physical Hilbert space. It offers two complementary derivations: a light-cone Green-Schwarz approach that identifies the transverse string coordinates with the eikonal oscillators, and a covariant Reggeon framework that captures the same physics via Reggeon exchange and the Reggeon vertex, with a detailed mapping between covariant states and the light-cone basis using DDF operators. The authors explicitly compute inelastic transitions from massless NS-NS states to the first two massive levels, reveal robust SO(8) selection rules, and demonstrate a consistent, level-by-level correspondence between covariant amplitudes and eikonal matrix elements. These results illuminate how tidal forces drive string excitations, preserve unitarity, and provide a concrete platform for exploring higher-level string dynamics and potential extensions to brane microstates or black-hole physics in the high-energy regime.

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.