Exact solutions and momentum couplings in the Dirac-Born-Infeld effective theory

TL;DR

This paper derives exact solutions in the Dirac-Born-Infeld effective theory, revealing how scalar fields and electromagnetic fields influence D-brane dynamics, decay rates, and stability, with implications for brane propagation and decay processes.

Contribution

It provides new exact solutions in the DBI theory showing how scalar and electromagnetic fields affect D-brane mass, decay, and stability, extending understanding of brane dynamics.

Findings

Effective mass of scalars decreases on moving D-branes.

Unstable D-branes decay slower at higher velocities.

Electromagnetic fields influence brane fluctuation modes and decay rates.

Abstract

We study the dynamics of a general scalar field, a tachyon or an ordinary scalar, in the presence of world-volume massless fields in the DBI effective theory by exploring their exact solutions. The obtained solutions indicate that the effective mass of the general scalar on a uniformly moving D-brane decreases, even to zero. For the tachyon case, the result implies that unstable D-branes decay slower when moving faster. The effective mass is also reduced on D-strings or in the space-independent case on arbitrarily dimensional D-branes with constant electromagnetic fields. The result for a tachyon indicates that the electric fields tend to slow down while the magnetic fields tend to expedite the decay process of unstable D-branes. In the spacetime-dependent case, D$p$-branes with $p\geq2$ in the presence of constant electromagnetic fields can fluctuate only in some restricted modes so that they propagate no faster than light. We also find solutions showing that D$p$-branes ($p\geq2$) carrying a beam of electromagnetic waves are propagating together with the electromagnetic waves. On such D$p$-branes, the tachyon gets stable while the massive scalar gets unstable if we demand their spacetime-dependent solutions to be real.