Tensors from K3 Orientifolds

TL;DR

The paper analyzes Type I compactifications on K3 orbifolds and shows that orientifold projections differ from the smooth K3 limit, yielding extra tensor multiplets localized at fixed points and introducing the nontrivial projection $\Omega' = \Omega J$. It then constructs a new $\mathbf{Z}_2$ orientifold with a consistency condition on Chan-Paton factors, builds a compact model with a mixed fixed-point structure connected to Dabholkar-Park solutions via T-duality, and clarifies the spectrum and tadpole charges of these configurations. Using D-brane probes, the work verifies that the local geometry near orbifold singularities is given by blown-up ALE spaces and derives the corresponding hyper-Kähler metrics, providing a geometric readout of the tensor content. Overall, the results illuminate how extra tensors arise in orientifolds of K3, classify $\mathbf{Z}_2$ singularities, and demonstrate a D-brane approach to extracting geometric data from string theory.

Abstract

Recently Gimon and Johnson (hep-th/9604129) and Dabholkar and Park (hep-th/9604178) have constructed Type I theories on K3 orbifolds. The spectra differ from that of Type I on a smooth K3, having extra tensors. We show that the orbifold theories cannot be blown up to smooth K3's, but rather $Z_2$ orbifold singularities always remain. Douglas's recent proposal to use D-branes as probes is useful in understanding the geometry. The $Z_2$ singularities are of a new type, with a different orientifold projection from those previously considered. We also find a new world-sheet consistency condition that must be satisfied by orientifold models.