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

TL;DR

This work uses perturbative string theory to study high-energy scattering of a massless closed string from a stack of Dp-branes, showing that open-string loop resummation induces an effective curved background described by the extremal p-brane metric. The authors derive an operator eikonal for the S-matrix by summing disk and annulus diagrams, reproduce the leading gravitational deflection and tidal excitations, and demonstrate exact agreement with classical geodesic and pp-wave analyses in the appropriate regimes. String corrections enter as Reggeized graviton exchanges, with subleading terms renormalizing the leading eikonal and encoding tidal effects; at large impact parameter these corrections preserve unitarity through exponentiation. The results establish a microscopic, unitary link between flat-space string amplitudes and the curved spacetime dynamics generated by Dp-branes, providing a controlled framework to explore gravitational scattering and its implications for black-hole physics.

Abstract

We extend previous techniques for calculations of transplanckian-energy string-string 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, we are able to explore various interesting regimes and to reproduce classical expectations, including tidal-force excitations, even beyond the leading-eikonal approximation.

Figures (4)

• Figure 1: Various qualitative regimes in the scattering of a closed string of fixed high energy off a stack of Dp-branes as a function, in a log-log plot, of $R_p$ and $b$, both taken to be bigger than the effective string scale $l_s(s)$. The different regions are discussed in the text.
• Figure 2: The string world-sheet is represented by the annulus between the outer circle of radius $1$ and the inner circle of radius $e^{-\pi\lambda}$. The two external states are represented by the two punctures located at $z_1$ and $z_2$.
• Figure 3: Diagram (a) contributes both to the leading ($\sim E^2$) and to the subleading ($\sim E$) terms in the S-matrix. Diagram (b) yields contributions scaling at most as $E$.
• Figure 4: The contributions of these diagrams to the S-matrix scale at most as $E$. The third diagram involves the exchange of a RR-field represented by the dashed lines. At high energies they combine and cancel exactly the leading term of diagram \ref{['feyn1']}(b).