Singular tachyon kinks from regular profiles

TL;DR

This paper shows how to derive Sen's singular tachyon kink solutions from regular profiles by carefully taking limits, highlighting the importance of limit order and potential choices in the process.

Contribution

It introduces a method to obtain singular tachyon kinks from regular profiles by controlling the limit process, challenging previous conditions on the potential.

Findings

Limit order determines the existence of singular solutions.

Regular profiles can approximate singular kinks via parameter limits.

The approach circumvents previous restrictions on tachyon potentials.

Abstract

We demonstrate how Sen's singular kink solution of the Born-Infeld tachyon action can be constructed by taking the appropriate limit of initially regular profiles. It is shown that the order in which different limits are taken plays an important role in determining whether or not such a solution is obtained for a wide class of potentials. Indeed, by introducing a small parameter into the action, we are able circumvent the results of a recent paper which derived two conditions on the asymptotic tachyon potential such that the singular kink could be recovered in the large amplitude limit of periodic solutions. We show that this is explained by the non-commuting nature of two limits, and that Sen's solution is recovered if the order of the limits is chosen appropriately.