Microstate Dependence of Scattering from the D1-D5 System

TL;DR

This paper studies how scattering from the D1-D5 system depends on its microstates, revealing that microstate-specific effects emerge at certain energy resolutions and providing bounds on these corrections.

Contribution

It introduces a detailed analysis of microstate dependence in D1-D5 scattering, including bounds on corrections and their relation to geometric features.

Findings

At high energy resolution, scattering is independent of microstates.

Microstate dependence appears at lower energy resolutions, with bounds proportional to the horizon area.

Numerical results show corrections scale with the square root of charges, without logarithmic factors.

Abstract

We investigate the question of distinguishing between different microstates of the D1-D5 system (with charges Q_1 and Q_5), by scattering with an incoherent beam, composed of a supergravity probe, with central energy E_0 and width (\Delta 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(\Delta 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 (\Delta 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 >> \Delta E >> (the average energy gap 1/{R [sqrt(Q_1Q_5)]}. For a typical state the bound is proportional to the area of the stretched horizon, [\sqrt(Q_1 Q_5)], up to [log (Q_1Q_5)] terms. Furthermore, when E_0 << (\Delta 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(Q_1Q_5)] 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.