Vanishing conditions for higher order couplings in heterotic theories

TL;DR

This paper identifies cohomological conditions in heterotic string compactifications that cause all higher order superpotential couplings to vanish, revealing unexpected suppression of interactions without known symmetries.

Contribution

It generalizes vanishing theorems for Yukawa couplings to all higher order couplings using cohomological criteria, providing new insights into superpotential structure.

Findings

Certain couplings vanish due to cohomological conditions

Some fields are absent from the perturbative superpotential

Infinite sets of couplings vanish without known symmetry explanations

Abstract

For compactifications of heterotic string theory, we elucidate simple cohomological conditions that lead to the vanishing of superpotential n-point couplings for all n. These results generalize some vanishing theorems for Yukawa couplings that have previously appeared in the literature to all higher orders. In some cases, these results are enough to show that certain fields do not appear in the perturbative superpotential at all. We illustrate our discussion with a number of concrete examples. In some cases, our results can be confirmed by showing that symmetries indeed forbid the couplings that vanish. In many, however, no such symmetries are known to exist and, as such, the infinite sets of vanishing couplings that are found are surprising from a four-dimensional perspective.