Perturbations and moduli space dynamics of tachyon kinks

TL;DR

This paper studies the fluctuation modes and moduli space dynamics of tachyon kinks on decaying unstable D-branes, revealing zero modes, instabilities, and a periodic decay process in the brane-antibrane system.

Contribution

It provides a detailed analysis of tachyon fluctuation spectra and moduli space trajectories for brane decay, highlighting zero modes and the zero-thickness limit behavior.

Findings

Eigenmodes are localized on the brane as thickness approaches zero.

Zero modes and low-lying excitations show a 4-fold degeneracy in the thin brane limit.

The decay process exhibits a periodic oscillation between unstable branes and brane-antibrane pairs.

Abstract

The dynamic process of unstable D-branes decaying into stable ones with one dimension lower can be described by a tachyon field with a Dirac-Born-Infeld effective action. In this paper we investigate the fluctuation modes of the tachyon field around a two-parameter family of static solutions representing an array of brane-antibrane pairs. Besides a pair of zero modes associated with the parameters of the solution, and instabilities associated with annihilation of the brane-antibrane pairs, we find states corresponding to excitations of the tachyon field around the brane and in the bulk. In the limit that the brane thickness tends to zero, the support of the eigenmodes is limited to the brane, consistent with the idea that propagating tachyon modes drop out of the spectrum as the tachyon field approaches its ground state. Low-lying excited states, including the zero modes, appear to show a 4-fold degeneracy in this limit. Finally, we also discuss the slow motion of the solution corresponding to the decay process in the moduli space, finding a trajectory which oscillates periodically between the unstable D-brane and the brane-antibrane pairs of one dimension lower.