Yukawa Couplings on Quintic Threefolds

TL;DR

The paper addresses the massless spectrum and Yukawa couplings in heterotic compactifications on quintic threefolds using bundles that deform $E=\mathcal{O}_X\oplus T X$, and connects these to Li–Yau torsion backgrounds through the Strominger system. It constructs the Li–Yau $SU(4)$ deformations $\mathcal{E}$, computes $H^*(X,\mathcal{E})$ and $H^*(X,\wedge^2\mathcal{E})$ for both generic and non-generic bundles, and analyzes the moduli-dependent Yukawa triple product $H^1(X,\mathcal{E})^{\otimes 2}\otimes H^1(X,\wedge^2\mathcal{E}) \to \mathbb{C}$, with explicit examples. For generic quintics, $H^1(X,\mathcal{E})$ has dimension $100$ and $H^*(X,\wedge^2\mathcal{E})=0$, while on a non-generic Dwork quintic one obtains $h^1(\mathcal{E})\neq0$ and $h^1(\wedge^2\mathcal{E})=h^2(\wedge^2\mathcal{E})=50$, with nonzero Yukawas that depend on the bundle moduli. The authors also prove that for every smooth quintic there exists a deformation $\mathcal{E}$ with non-vanishing Yukawa couplings, via Li–Yau stability criteria, implying heterotic vacua with torsion can support nonzero Yukawa interactions across the quintic moduli space.

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.