Exact absorption probabilities for the D3-brane

TL;DR

This paper derives exact formulas for absorption probabilities of a scalar field interacting with a D3-brane, using Mathieu functions, and explores implications for D3-brane world-volume theories.

Contribution

It provides an exact analytical solution for absorption probabilities in the D3-brane background using Mathieu functions, advancing understanding of brane interactions.

Findings

Exact absorption probabilities expressed via Mathieu functions

Algorithm for low-energy expansion of absorption probabilities

Implications for D3-brane world-volume theory

Abstract

We consider a minimal scalar in the presence of a three-brane in ten dimensions. The linearized equation of motion, which is just the wave equation in the three-brane metric, can be solved in terms of associated Mathieu functions. An exact expression for the reflection and absorption probabilities can be obtained in terms of the characteristic exponent of Mathieu's equation. We describe an algorithm for obtaining the low-energy behavior as a series expansion, and discuss the implications for the world-volume theory of D3-branes.