Scattering off Chamblin-Reall Branes

TL;DR

This paper analyzes how dilaton-graviton waves scatter off a thin brane in three-dimensional spacetime, revealing complex reflection, transmission, and absorption behaviors related to strongly coupled theories and holography.

Contribution

It provides a detailed analysis of wave scattering in holographic models with branes, highlighting the effects of dimensionality and boundary conditions on flux redistribution.

Findings

For d=2, the interface acts like a translucent window with diffuse scattering.

In d=4, the scattering is sensitive to infrared boundary conditions, requiring regularization.

The equations suggest similar flux redistribution in regularized d=4 scenarios.

Abstract

We study the linearized scattering of dilaton-graviton waves from a thin brane in three-dimensional spacetime. Holographically, the setup models scattering from an interface in a family of strongly coupled theories related to dimensional reductions of higher-dimensional $AdS_{d+2}$ gravity. Unlike the pure $AdS_3$ case, for $d>1$ the physical bulk mode allows incident radiation to be redistributed into reflected, transmitted, and evanescent components. For the $d=2$ background, we obtain a controlled solution in which the interface acts like a rough translucent window, producing diffuse angular scattering and absorption into surface modes. From the dual perspective, the scattering process is suggestive of dissipative flow toward the infrared. For $d=4$, the same analysis reveals a sensitivity to the infrared boundary condition, suggesting that the singular zero-temperature geometry must be regulated in order to have a well-defined scattering process. The structure of the equations nevertheless suggests that a regulated $d=4$ problem may exhibit the same qualitative redistribution of incident flux.