Evolution of Tachyon Kink with Electric Field

TL;DR

This paper studies how an electric field influences the decay and stability of tachyon kinks on a D1-brane wrapped on a circle, revealing a critical flux value that determines whether the kink destabilizes or remains stable.

Contribution

It numerically analyzes the decay process of tachyon kinks with electric flux, identifying a critical electric flux that stabilizes the kink against decay.

Findings

Below critical flux, tachyon kink decays into lower-dimensional branes.

Above critical flux, tachyon kink remains stable.

The decay process resembles caustic formation in similar systems.

Abstract

We investigate the decay of an inhomogeneous D1-brane wrapped on a $S^1$ with an electric field. The model that we consider consists of an array of tachyon kink and anti-kink with a constant electric flux. Beginning with an initially static configuration, we numerically evolve the tachyon field with some perturbations under a fixed boundary condition at diametrically opposite points on the circle $S^1$. When the electric flux is smaller than the critical value, the tachyon kink becomes unstable; the tachyon field rolls down the potential, and the lower dimensional D0- and $\bar {\rm D}0$-brane become thin, which resembles the caustic formation known for this type of the system in the literature. For the supercritical values of the electric flux, the tachyon kink remains stable.