A Note on Toroidal Compactifications of the Type I Superstring and Other Superstring Vacuum Configurations with 16 Supercharges

TL;DR

This work argues that the moduli space of string vacua with 16 supercharges contains multiple disconnected components that can be understood through BPS un-orientifolds—toroidal Type I compactifications with a quantized NS-NS background $B_{ij}$, yielding rank-reduced gauge groups. By embedding these constructions in a rational CFT framework, the paper derives a Chan–Paton reduction $N_{CP} = 32 \times 2^{-b/2}$ with $b = \mathrm{rank}(\widehat{B})$ (an even integer) and connects the phenomenon to $\omega_2({\cal V})$ and discrete torsion, providing a closed-string picture for what otherwise appears as open-string data. It then maps these components to Type II vacua, both $(2,2)$ and asymmetric $(4,0)$ models, and shows via dualities (including U-duality) how some Type II constructions correspond to Type I configurations without open strings or to CHL heterotic models with the same vector multiplet content. The analysis clarifies how non-perturbative states and duality webs organize the vacuum landscape and suggests further links to M-theory and F-theory compactifications, with implications for vacuum selection beyond perturbation theory.

Abstract

We show that various disconnected components of the moduli space of superstring vacua with 16 supercharges admit a rationale in terms of BPS un-orientifolds, i.e. type I toroidal compactifications with constant non-vanishing but quantized vacuum expectation values of the NS-NS antisymmetric tensor. These include various heterotic vacua with reduced rank, known as CHL strings, and their dual type II (2,2) superstrings below D=6. Type I vacua without open strings allow for an interpretation of several disconnected components with N_V=10-D. An adiabatic argument relates these unconventional type I superstrings to type II (4,0) superstrings without D-branes. The latter are connected by U-duality below D=6 to type II (2,2) superstrings. We also comment on the relation between some of these vacua and compactifications of the putative M-theory on unorientable manifolds as well as F-theory vacua.