Microstate dependence of scattering from the D1-D5 system

Abstract

We investigate the question of distinguishing between different microstates of the D1-D5 system with charges Q₁ and Q₅, by scattering off the system a supergravity mode which is a minimally coupled scalar in the leading supergravity approximation. The scattering is studied in the dual CFT description in the orbifold limit for finite R, where R is the radius of the circle on which the D1 branes are wrapped. Even though the system has discrete energy levels for finite R, an absorption probability proportional to time is found when the ingoing beam has a finite width ΔE which is much larger than the inverse of the time scale T. When RΔE » 1, the absorption crosssection is found to be independent of the microstate and identical to the leading semiclassical answer computed from the naive geometry. For smaller ΔE, the answer depends on the particular microstate, which we examine for typical as well as for atypical microstates and derive an upper bound for the leading correction for either a Lorentzian or a Gaussian energy profile of the incoming beam. When 1/R » ΔE » the average energy gap (1/(R(Q₁Q₅)^1/2)), we find that in a typical state the bound is proportional to the area of the stretched horizon, (Q₁Q₅)1/2, up to log(Q₁Q₅) terms. Furthermore, when the central energy in the incoming beam, E₀, is much smaller than ΔE, the proportionality constant is a pure number independent of all energy scales. Numerical calculations using Lorentzian profiles show that the actual value of the correction is in fact proportional to (Q₁Q₅)^1/2 without the logarithmic factor. We offer some speculations about how this result can be consistent with a resolution of the naive geometry by higher derivative corrections to supergravity.