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 with an incoherent beam, composed of a supergravity probe, with central energy E0 and width ( E). 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. When R( E) >> 1, the absorption cross-section is found to be independent of the microstate and identical to the leading semiclassical answer computed from the naive geometry. For smaller ( E), the answer depends on the particular microstate, which we examine for both typical and atypical microstates. We derive an upper bound for the leading correction to the cross-section when 1/R >> E >> (the average energy gap 1/R [sqrt(Q1Q5)]. For a typical state the bound is proportional to the area of the stretched horizon, [(Q1 Q5)], up to [log (Q1Q5)] terms. Furthermore, when E0 << ( E), 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 [sqrt(Q1Q5)] 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.