Generalized Vanishing Theorems for Yukawa Couplings in Heterotic Compactifications

TL;DR

This paper generalizes vanishing theorems for Yukawa couplings in heterotic string compactifications, revealing their topological and geometric origins through an algebro-geometric approach, applicable beyond previous constraints.

Contribution

It introduces a new algebro-geometric method to derive and extend vanishing theorems for Yukawa couplings, including cases where bundles do not descend from ambient space.

Findings

Vanishing Yukawa textures are widespread in heterotic compactifications.

The approach applies to bundles not descending from ambient space.

Multiple geometric constraints influence Yukawa coupling textures.

Abstract

Heterotic compactifications on Calabi-Yau threefolds frequently exhibit textures of vanishing Yukawa couplings in their low energy description. The vanishing of these couplings is often not enforced by any obvious symmetry and appears to be topological in nature. Recent results in the literature used differential geometric methods to explain the origin of some of this structure. A vanishing theorem was given which showed that the effect could be attributed, in part, to the embedding of the Calabi-Yau manifolds of interest inside higher dimensional ambient spaces, if the gauge bundles involved descended from vector bundles on those larger manifolds. In this paper, we utilize an algebro-geometric approach to provide an alternative derivation of some of these results, and are thus able to generalize them to a much wider arena than has been considered before. For example, we consider cases where the vector bundles of interest do not descend from bundles on the ambient space. In such a manner we are able to highlight the ubiquity with which textures of vanishing Yukawa couplings can be expected to arise in heterotic compactifications, with multiple different constraints arising from a plethora of different geometric features associated to the gauge bundle.