Gravitational lensing by p-branes

TL;DR

This paper investigates the scattering of R-R gauge bosons by p-branes, demonstrating stringy properties and confirming that D-branes serve as exact descriptions of extremal p-branes, with special insights into D-instantons and black hole entropy.

Contribution

It provides a detailed string-theoretic analysis of p-brane scattering, confirming the correspondence with supergravity solutions and highlighting the unique behavior of D-instantons.

Findings

All p >= 0 branes exhibit stringy Regge behavior.

Scattering amplitudes match supergravity solutions at small momentum transfer.

D-instantons are point-like and reproduce full string calculations.

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.