Gravitational lensing by p-branes

TL;DR

This work computes disk-level scattering of RR gauge bosons off Dirichlet $p$-branes and demonstrates that RR and NS-NS scattering share Regge behavior, with low-momentum amplitudes matching extremal RR-charged $p$-brane solutions. It provides a general RR $n$-form scattering formula in terms of gamma-function prefactors and traces $P_1,P_2$ of gamma matrices, and shows the D-instanton case ($p=-1$) exhibits point-like behavior with exact field-theory reproduction. The authors further show that the same low-energy dynamics describe scattering off extremal black $p$-branes, reproducing the $1/t$ pole and polarization structure from classical backgrounds, and discuss how towered open-string excitations encode a discrete spectrum related to horizon dynamics. They relate these results to entropy of non-extremal ten-dimensional black holes derived from exciting the 0-brane, highlighting the broader significance for the D-brane-black-hole correspondence and non-perturbative string dynamics.

Abstract

The scattering of R-R gauge bosons off of Dirichlet p-branes is computed to leading order in the string coupling. The results are qualitatively similar to those found in the scattering of massless NS-NS bosons: all p-branes with p >= 0 exhibit stringy properties, in particular the Regge behavior. Both the R-R and NS-NS scattering amplitudes agree in the limit of small momentum transfer with scattering off the extremal R-R charged p-brane solutions found in the low-energy supergravities. We interpret this as evidence that Dirichlet-branes are an exact world-sheet description of the extremal p-branes. The -1-brane (D-instanton) is a special object which, unlike all other Dirichlet-branes, exhibits point-like behavior. We find the R-R charged instanton solution to type IIB supergravity and confirm that the field theoretic scattering off of this solution miraculously reproduces the full stringy calculation. As an aside, we include a discussion of the entropy of non-extremal black holes in ten dimensions, produced by exciting the 0-brane. We show that, for large black holes, the entropy grows linearly with the black hole mass.

Figures (1)

• Figure 1: Scattering of R-R gauge bosons off a $p$-brane. The low momentum transfer limit is mediated as shown by $t$-channel exchange of a massless mode.