Heterotic string on the simplest Calabi-Yau manifold and its orbifold limits

Abstract

We study the heterotic string on the simplest (nontrivial) Calabi-Yau manifold K3 and its orbifold limits. We set the background gauge connection equal to the spin connection. The massless spectrum of the field theory that is the low-energy limit of the ${\mathrm{E}}_8$⊗${\mathrm{E}}_8$ string is derived on K3. Some terms in the effective Lagrangian for the massless modes are shown to be determined by the topology of K3. Several orbifold limits of K3 are described as $T^4$/$Z_l$, after the singular points are removed and replaced by well-behaved spaces. Massless spectra of the full string theory on these orbifolds are obtained. Orbifold and manifold results are compared. Knowing how to blow up the orbifolds determines much of the full string massless spectrum, including information about the spectra of the individual twisted sectors.