Perturbations and moduli space dynamics of tachyon kinks

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. The zero modes, and other low-lying excited states, show a 4-fold degeneracy in this limit, which can be identified with some of the massless superstring modes in the brane-antibrane system. 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.

Inhomogeneous tachyon condensation

“…For fixed V m , T ′ tends to infinity at kinks and anti-kinks, where △x = nπ/β, as V 0 → 0, which is consistent with the slow motion analysis on the moduli space of [7].…”

“…The condensation process in the inhomogeneous case has also been studied. It has been realised that the equation of motion from the DBI action leads to solitonic solution with kinks and anti-kinks [4,5,6,7]. At the kinks and anti-kinks, the field remains zero, and become daughter branes of one dimension lower at the end of the condensation.…”

“…While the field in between them grows with time and tends to infinity. The huge difference of the field values between these two areas makes the field gradient at kinks and anti-kinks very large and in fact can be semi-analytically shown to lead to infinity in finite time [8,7]. The existence of this kind of singularity prevents straightforward numerical integration of the space-time dependent field equation [9,10].…”

Exact solutions in the Dirac-Born-Infeld effective theory and the fate of tachyon

“…It is also a solution to the equation φ + αφ = 0. But there is a difference: the solution to the equation φ + αφ = 0 can be an arbitrary combination of the solution (9) or (10) of different momenta k, while the solution to the equation ( 7) can be the solution ( 9) or (10) only of a single momentum k. Any combination of the solution is not a solution to Eq. ( 7) because such a solution cannot make the intersecting terms in Eq.…”

“…At kinks, the tachyon field vanishes but the field gradient grows with time. Towards the end of condensation, the kinks become infinitely thin and the field gradient at kinks grows to infinity [8,9,10]. In regions away from kinks and anti-kinks, the field grows to infinity at the end of condensation, reaching the vacuum.…”