An Orbifold and an Orientifold of Type IIB Theory on K3 $\times$ K3

TL;DR

This paper explores compactifications of type IIB superstring theory on K3 $ imes$ K3, analyzing their spectra, anomaly cancellation, and dualities, including orbifold and orientifold projections, and M-theory duals.

Contribution

It provides a detailed analysis of the massless spectra and anomaly cancellation for type IIB on K3 $ imes$ K3, including orbifold and orientifold models, and discusses dualities with M-theory.

Findings

The models are free of gravitational anomalies.

Orbifold and orientifold spectra match and are anomaly-free.

Duality relations with M-theory are established.

Abstract

We consider the compactification of type IIB superstring theory on K3 $\times$ K3. We obtain the massless spectrum of the resulting two dimensional theory and show that the model is free of gravitational anomaly. We then consider an orbifold and an orientifold projection of the above model and find that their spectrum match identically and are anomaly-free as well. This gives a dual pair of type IIB theory in two dimensions and can be understood as a consequence of SL(2, Z) symmetry of the ten dimensional theory. We also point out the M-theory duals of the type IIB compactifications considered here.