TASI Lectures on Non-BPS D-Brane Systems

TL;DR

Schwarz surveys non-BPS D-brane configurations in Type II and Type I string theories, arguing that tachyon condensation yields both stable and unstable solitons and that D-brane charges are naturally classified by K-theory groups (including $KO$ and its variants). The talk highlights a non-BPS D0 in Type I carrying a $Z_2$ charge, the role of T-duality and orientifolds such as ${\rm O}9$, ${\rm O}8$, and the moduli spaces of 16-supercharge vacua in $d=9$ and $d=8$. It also discusses potential pitfalls for D$7$ and D$8$ branes predicted by K-theory in Type I', and how spacetime-filling branes modify the story. Altogether, K-theory provides a robust framework for D-brane charges beyond cohomology and reveals rich nonperturbative structure even in non-supersymmetric regimes.

Abstract

In this set of lectures various properties of D-branes are discussed. After reviewing the basics, we discuss unstable D-brane/anti-D-brane systems, a subject pioneered by Sen. Following him, we discuss the construction of the non-BPS D0-brane in type I theory. This state is stable since it carries a conserved Z_2 charge. The general classification of D-brane charges using K-theory is discussed. The results for the type I theory, and the T-dual type I' theory, are emphasized. Compactification of type I on a circle or torus gives a theory with 16 supersymmetries in 9d or 8d. In each case the moduli space has three branches. The spectrum of non-BPS D-branes are different for each of these branches. We conclude by pointing out some problems with the type I D7-brane and D8-brane predicted by K-theory.