Orientifold Planes, Type I Wilson Lines and Non-BPS D-branes

TL;DR

The paper addresses the existence of negatively charged orientifold planes with stuck D-branes for p≥6, resolving a puzzle by showing $ ilde{O6}^-$ planes exist in massive IIA with odd cosmological constant while $ ilde{O}7^-$ and $ ilde{O}8^-$ do not. It develops a cohesive framework combining Type I Wilson lines, T-duality, and discrete torsions to classify compatible configurations and their RR/NS-NS flux content, and links these to the physics of non-BPS D-branes via KO-theory and tachyon condensation. A central mechanism is that wrapped branes and domain walls shift discrete torsions and RR charges, enabling transfers between plane types and the transfer of stuck D-branes as magnetic flux on higher-dimensional branes. The work highlights a deep interplay between non-perturbative Type I dynamics, orientifold classifications, and flux quantization, with implications for the global consistency of orientifold configurations and their non-BPS sectors.

Abstract

There is a longstanding puzzle concerned with the existence of Op~-planes with p>=6, which are orientifold p-planes of negative charge with stuck Dp-branes. We study the consistency of configurations with various orientifold planes and propose a resolution to this puzzle. It is argued that O6~-planes are possible in massive IIA theory with odd cosmological constant, while O7~-planes and O8~-planes are not allowed. Various relations between orientifold planes and non-BPS D-branes are also addressed.

Figures (5)

• Figure 1: Each possible configuration of O$5$-planes is the same with one of these up to rotation. The cubes spread in the $x^1$,$x^2$,$x^3$ directions and left (right) ones are located at $x^4=-1$ ($+1$). O$5$-planes are located at the apexes of the cubes, and the bullets represent $\widetilde{\hbox{O}5}^-$-planes. We have 1 (a)-type, 12 (b)-type, 8 (c)-type, 2 (d)-type, 8 (e)-type and 1 (f)-type configurations. (b), (c), (d) and (e) are equivalent to each other via modular transformations.
• Figure 2:
• Figure 3: The relations (i) and (ii). The types of O$p$-planes are flipped after condensation of the tachyonic modes on the 'non-BPS D-branes'.
• Figure 4: Descriptions of the 'non-BPS D-branes' in ${\bf T}^3/{\bf Z}_2$ orientifold using D8-branes. The outside region divided by the D8-branes is in the background with odd cosmological constant.
• Figure 5: Transfer of stuck D-branes. The system with eight $\widetilde{\hbox{O}6}^-$-planes can be continuously deformed to that with eight O$6^-$-planes.