We study the topological heterotic ring in (0,2) Landau-Ginzburg models without a (2,2) locus. The ring elements correspond to elements of the Koszul cohomology groups associated to a zero-dimensional ideal in a polynomial ring, and the computation of half-twisted genus zero correlators reduces to a map from the first nontrivial Koszul cohomology group to complex numbers. This map is a generali...

We classify the simply-connected supersymmetric parallelisable backgrounds of heterotic supergravity. They are all given by parallelised Lie groups admitting a bi-invariant lorentzian metric. We find examples preserving 4, 8, 10, 12, 14 and 16 of the 16 supersymmetries.

In this short review, we outline three sets of developments in understanding heterotic string compactifications. First, we outline recent progress in heterotic analogues of quantum cohomology computations. Second, we discuss a potential swampland issue in heterotic strings, and new heterotic string constructions that can be used to fill in the naively missing theories. Third, we discuss recent ...

Heterotic groups are necessary for high vigor in hybrid rice. However, hybrids produced from crosses between parents different rice subspecies (i.e., Indica × Japonica) have extensive incompatibility issues exhibited by low seed sets. The study objectives were to evaluate the heterosis grain yield and yield-related traits parental genetic distances (PGDs) demonstrate heterotic group approach Fr...

We construct heterotic string theories on spacetimes of the form Rd−1,1×N = 2 linear dilaton, where d = 6, 4, 2, 0. There are two lines of supersymmetric theories descending from the two supersymmetric ten-dimensional heterotic theories. These have gauge groups which are lower rank subgroups of E8×E8 and SO(32). On turning on a (2, 2) deformation which makes the two dimensional part a smooth SL...

We study compactifications of F-theory on certain Calabi–Yau threefolds. We find that N = 2 dualities of type II/heterotic strings in 4 dimensions get promoted to N = 1 dualities between heterotic string and F-theory in 6 dimensions. The six dimensional heterotic/heterotic duality becomes a classical geometric symmetry of the Calabi–Yau in the F-theory setup. Moreover the F-theory compactificat...

The objectives of the present study were to determine heterotic groups of germplasm lines of tropical maize by test crosses and by simple sequence repeat (SSR) markers and to compare five grouping methods of heterogeneous maize. Sixteen lines of nine populations in the S5 generation were evaluated in test crosses with three testers. The results of four experimental trials over two years were us...