Remarks on Non-BPS D-Branes

TL;DR

This paper argues that K-theory provides the natural framework for classifying conserved D-brane charges in string theory, including predictions of non-BPS branes such as a D8-brane in type I. It analyzes unstable high-dimensional non-BPS branes via tachyon condensation on brane–antibrane pairs and shows how Type I D0-branes arise as tachyon kinks in a D1–anti-D1 system, carrying a ${\bf Z}_2$ charge with a mass scale set by the coupling $g$ and a critical radius $R_c=1/\sqrt{2}$. Using KO-theory, the charges are organized by ${\widetilde{KO}(S^{9-p})}$, yielding specific group structures (e.g., ${\mathbb{Z}}$ for $p=1,5,9$ and ${\mathbb{Z}}_2$ for $p=0,7,8$) and a fixed total RR 9-brane charge of 32 for Type I. The discussion of ${\rm D}8$-brane reveals its instability due to 32 tachyons in the D8–D9 sector and explores a domain-wall interpretation linked to D-instantons and Bott periodicity, highlighting how tachyon dynamics can invalidate naive higher-dimensional non-BPS branes despite the K-theory classification.

Abstract

Following Sen's discovery of various stable non-BPS D-branes, K-theory has been shown to be the appropriate mathematical framework for classifying conserved D-brane charges. The classification accounts for known D-branes and predicts some new ones including a D8-brane in type I superstring theory. After briefly reviewing these developments, we discuss certain issues pertaining to the D8-brane, which is unstable.