BPS D-branes from an Unstable D-brane

TL;DR

This paper finds exact tachyon kink solutions on unstable D-branes with gauge fields in flat and curved backgrounds, identifying BPS bound states and composite brane configurations in string theory.

Contribution

It provides explicit solutions for tachyon kinks on unstable D-branes, including BPS states and composites in curved backgrounds, advancing understanding of brane decay and bound states.

Findings

Identified BPS D($p$-1)F1 bound states as thick branes with flux.

Constructed solutions in flat space with various electromagnetic field configurations.

Described composite D-branes and strings in curved background, including BPS limits.

Abstract

We search for exact tachyon kink solutions of DBI type effective action describing an unstable D-brane with worldvolume gauge field turned in both the flat and a curved background. There are various kinds of solutions in the presence of electromagnetic fields in the flat space, such as periodic arrays, topological tachyon kinks, half kinks, and bounces. We identify a BPS object, D($p$-1)F1 bound state, which describes a thick brane with string flux density. The curved background of interest is the ten-dimensional lift of the Salam-Sezgin vacuum and, in the asymptotic limit, it approaches ${\rm R}^{1,4}\times {\rm T}^2\times {\rm S}^3$. The solutions in the curved background are identified as composites of lower-dimensional D-branes and fundamental strings, and, in the BPS limit, they become a D4D2F1 composite wrapped on ${\rm R}^{1,2}\times {\rm T}^2$ where ${\rm T}^2$ is inside ${\rm S}^3$.