A bstract We study coupling selection rules of chiral matter fields in heterotic string theory with standard embedding. These selection rules are determined by topological properties of Calabi-Yau threefolds. We classify coupling selection rules on complete intersection Calabi-Yau threefolds for h 1,1 ≤ 5. It is found that all of these selection rules for h 1,1 ≤ 5 are understood by combinations of only five types of fusion rules.
Dong et al. (2025) studied this question.