D-Branes and their Absorptivity in Born-Infeld Theory

TL;DR

This paper analyzes the stability and absorptivity of D-branes within Born-Infeld theory by deriving fluctuation equations, solving a modified Mathieu equation, and providing explicit scattering amplitudes, extending understanding to high-energy regimes.

Contribution

It introduces a high-energy expansion of the Floquet exponent for the Mathieu equation and applies it to D-brane fluctuation analysis, filling a gap in previous studies.

Findings

Derived explicit S-matrix and absorption amplitudes

Confirmed physical expectations through numerical validation

Extended analysis to high-energy fluctuations of D-branes

Abstract

Standard methods of nonlinear dynamics are used to investigate the stability of particles, branes and D-branes of abelian Born-Infeld theory. In particular the equation of small fluctuations about the D-brane is derived and converted into a modified Mathieu equation and - complementing earlier low-energy investigations in the case of the dilaton-axion system - studied in the high-energy domain. Explicit expressions are derived for the S-matrix and absorption and reflection amplitudes of the scalar fluctuation in the presence of the D-brane. The results confirm physical expectations and numerical studies of others. With the derivation and use of the (hitherto practically unknown) high energy expansion of the Floquet exponent our considerations also close a gap in earlier treatments of the Mathieu equation.