Tachyon condensation in unstable type I D-brane systems

TL;DR

This work classifies eight unstable Type I D-brane systems by determining their gauge groups and tachyon representations, and shows how tachyon vacuum topology encodes lower-dimensional D-brane charges via real K-theory. It extends the Type II complex K-theory relations to KO-groups by identifying vacuum manifolds with real classifying spaces and demonstrating a systematic shift between vacuum topology and KO^{-n} groups. The analysis clarifies the role of background D9-branes, revealing how they modify the vacuum structure and lead to gauge-field configurations that carry D-brane charges rather than relying on tachyon topology alone. Together, these results provide a unified, real-K-theory framework for understanding tachyon condensation and D-brane charges in unstable Type I systems, with implications for soliton spectra and potential M-theory connections.

Abstract

Type I string theory provides eight classes of unstable D-brane systems. We determine the gauge group and tachyon spectrum for each one, and thereby describe the gauge symmetry breaking pattern in the low-energy world-volume field theory. The topologies of the resulting coset vacuum manifolds are related to the real K-theory groups KO^{-n}, extending the known relations between the Type II classifying spaces BU and U and the complex K-theory groups K^0 and K^{-1}. We also comment on the role of the background D9-branes.