Yukawa Couplings on Quintic Threefolds

Abstract

We compute the particle spectrum and some of the Yukawa couplings for a family of heterotic compactifications on quintic threefolds X involving bundles that are deformations of TX+O_X. These are then related to the compactifications with torsion found recently by Li and Yau. We compute the spectrum and the Yukawa couplings for generic bundles on generic quintics, as well as for certain stable non-generic bundles on the special Dwork quintics. In all our computations we keep the dependence on the vector bundle moduli explicit. We also show that on any smooth quintic there exists a deformation of the bundle TX+O_X whose Kodaira-Spencer class obeys the Li-Yau non-degeneracy conditions and admits a non-vanishing triple pairing.