In this technical note we describe a pair of results on heterotic compactifications. First, we give an example demonstrating that the usual statement of the anomaly-freedom constraint for perturbative heterotic compactifications (meaning, matching second Chern characters) is incorrect for compactifications involving torsion-free sheaves. Secondly, we correct errors in the literature regarding t...

Abstract Forty-five African or Asian origin pearl millet populations bred either in Africa Asia were investigated to generate information on heterotic pools. They clustered into seven groups (G1 G7) when genotyped, using 29 highly polymorphic SSRs. Fourteen parental representing these marker-based crossed diallel mating design 91 population hybrids. The hybrids evaluated at three locations Indi...

We re-examine the question of heterotic heterotic string duality in six dimensions and argue that the E8 ×E8 heterotic string, compactified on K3 with equal instanton numbers in the two E8’s, has a self-duality that inverts the coupling, dualizes the antisymmetric tensor, acts non-trivially on the hypermultiplets, and exchanges gauge fields that can be seen in perturbation theory with gauge fie...

In this paper we discuss some aspects of N = 1 type I-heterotic string duality in four dimensions. We consider a particular example of a (weak-weak) dual pair where on the type I side there are only D9-branes corresponding to perturbative heterotic description in a certain region of the moduli space. We match the perturbative type I and heterotic tree-level massless spectra via giving certain s...

We review the derivation and the basic properties of the perturbative prepotential in N=2 compactifications of the heterotic superstring. We discuss the structure of the perturbative monodromy group and the embedding of rigidly supersymmetric monodromies associated with enhanced gauge groups, at both perturbative and non-perturbative level.

Two classes of stringy instanton effects, stronger than standard field theory instantons, are identified in the heterotic string theory. These contributions are established using type IIA/heterotic and type I/heterotic dualities. They provide examples for the heterotic case of the effects predicted by Shenker based on the large-order behavior of perturbation theory. The corrections vanish as th...

In this paper we discuss some aspects of N = 1 type I-heterotic string duality in four dimensions. We consider a particular example of a (weak-weak) dual pair where on the type I side there are only D9-branes corresponding to perturbative heterotic description in a certain region of the moduli space. We match the perturbative type I and heterotic tree-level massless spectra via giving certain s...

We review the duality between heterotic and F–theory string vacua with N = 1 space-time supersymmetry in eight, six and four dimensions. In particular, we discuss two chains of four-dimensional F–theory/heterotic dual string pairs, where F–theory is compactified on certain elliptic Calabi-Yau fourfolds, and the dual heterotic vacua are given by compactifications on elliptic Calabi-Yau threefold...

Pearl millet is a climate resilient crop and one of the most widely grown millets worldwide. Heterotic hybrid development is one of the principal breeding objectives in pearl millet. In a maiden attempt to identify heterotic groups for grain yield, a total of 343 hybrid parental [maintainer (B-) and restorer (R-)] lines were genotyped with 88 polymorphic SSR markers. The SSRs generated a total ...