Yukawa Couplings in Heterotic Compactification

TL;DR

This paper introduces an algebraic, computer-implementable method for efficiently calculating Yukawa couplings in heterotic string compactifications on Calabi-Yau three-folds, facilitating large-scale automated analysis.

Contribution

It provides a practical algorithm for computing Yukawa couplings in heterotic compactifications, applicable to a broad class of Calabi-Yau manifolds with non-standard embeddings.

Findings

Algorithm successfully computes Yukawa couplings for various models.

Method enables automated large-scale analysis of heterotic compactifications.

Applicable to positive monads over favourable complete intersection Calabi-Yaus.

Abstract

We present a practical, algebraic method for efficiently calculating the Yukawa couplings of a large class of heterotic compactifications on Calabi-Yau three-folds with non-standard embeddings. Our methodology covers all of, though is not restricted to, the recently classified positive monads over favourable complete intersection Calabi-Yau three-folds. Since the algorithm is based on manipulating polynomials it can be easily implemented on a computer. This makes the automated investigation of Yukawa couplings for large classes of smooth heterotic compactifications a viable possibility.