Moduli Dependent Spectra of Heterotic Compactifications

Abstract

Explicit methods are presented for computing the cohomology of stable, holomorphic vector bundles on elliptically fibered Calabi-Yau threefolds. The complete particle spectrum of the low-energy, four-dimensional theory is specified by the dimensions of specific cohomology groups. The spectrum is shown to depend on the choice of vector bundle moduli, jumping up from a generic minimal result to attain many higher values on subspaces of co-dimension one or higher in the moduli space. An explicit example is presented within the context of a heterotic vacuum corresponding to an SU(5) GUT in four-dimensions.

Figures (2)

• Figure 1: In 100,000 random integer initializations of the matrix $M_2$, the numbers of occurrences of the various values of $n_{\overline{5}}$ are plotted. We see that the generic value 37 dominates by far.
• Figure 2: A subspace of moduli space spanned by $\phi^{[(4)1]}_{p=1,2}$, $\phi^{[(4)2]}_{q=1,2,3}$ and $\phi^{[(4)3]}_{r=1,2,3,4}$. Generically, in the bulk, $n_{\bar{5}} = 37$, its minimal value. As we restrict to various planes and intersections thereof, we are confining ourselves to special sub-spaces of co-dimension one or higher. In these subspaces, the value of $n_{\bar{5}}$ can increase dramatically.