The fate of the type I non-BPS D7-brane

TL;DR

The paper analyzes the fate of Type I non-BPS D7 and D8 branes carrying a non-trivial Z2 K-theory charge, showing tachyon condensation dissolves them into topologically non-trivial D9-brane gauge configurations. In non-compact setups the decay runs to infinity, while toroidal transverse spaces yield a final supersymmetric Z2 toron with vanishing Chern classes, revealing a deep link between K-theory torsion and M-theory cohomology. It extends the analysis to related systems including lower-dimensional O$p$-planes and the USp(32) theory, and develops a detailed M-theory perspective on non-BPS states, K-theory versus cohomology, and NS-NS/RR charge transmutation via the Atiyah-Hitchin manifold. The work suggests a broader framework where string theory K-theory charges emerge from and are constrained by M-theory cohomology, with implications for charge classification, tachyon dynamics, and potential SUSY restoration in compactifications.

Abstract

We describe the fate of the Type I non-BPS D7-brane, which is tachyonic but carries a non-trivial K-theory $\IZ_2$ charge. It decays to topologically non-trivial gauge field configurations on the background D9-branes. In the uncompactified theory the decay proceeds to infinity, while with a transverse torus the decay reaches a final state, a toron gauge configuration with vanishing Chern classes but non-trivial $\IZ_2$ charge. A similar behaviour is obtained for the type I non-BPS D8-brane, and other related systems. We construct explicit examples of type IIB orientifolds with non-BPS D7-branes, which are hence non-supersymmetric, but for which supersymmetry is restored upon condensation of the tachyon. We also report on the interesting structure of non-BPS states of type IIA theory in the presence of an O6-plane, their M-theory lifts, the relation between string theory K-theory and M-theory cohomology, and its interplay with NS-NS charged objects. We discuss several new effects, including: i) transmutation between NS-NS and RR torsion charges, ii) non-BPS states classified by K-theory but not by cohomology in string theory, but whose lift to M-theory is cohomological.

Figures (4)

• Figure 1: Schematic picture of the decay of the type I ${\widehat{{\rm D}7}}$-brane in the type I and T-dual type I' pictures
• Figure 2: Schematic picture of ${\bf X_{AH}}$, a) as a topological space, b) when endowed with a hyperkahler metric.
• Figure 3: M-theory lift of the RR and NS-NS 4-branes as M5-brane in non-trivial 1-cycles in ${\bf X_{AH}}$.
• Figure 4: Schematic picture of the M-theory $\bf Z_2$ charged configuration of an M2-brane in a torsion 3-cycle in ${\bf X_{AH}}$.