Discrete Symmetries of Complete Intersection Calabi-Yau Manifolds

TL;DR

This paper classifies non-freely acting discrete symmetries of complete intersection Calabi-Yau manifolds, revealing their prevalence and variety, which are important for string theory compactifications and four-dimensional model building.

Contribution

It provides the first systematic classification of non-freely acting discrete symmetries on these manifolds, identifying common groups and their potential roles in string-derived models.

Findings

Non-freely acting symmetries occur in 381 out of 1695 quotients.

Nine discrete groups with orders from 2 to 18 are identified.

Both regular and R-symmetries are observed.

Abstract

In this paper, we classify non-freely acting discrete symmetries of complete intersection Calabi- Yau manifolds and their quotients by freely-acting symmetries. These non-freely acting symmetries can appear as symmetries of low-energy theories resulting from string compactifications on these Calabi-Yau manifolds, particularly in the context of the heterotic string. Hence, our results are relevant for four-dimensional model building with discrete symmetries and they give an indication which symmetries of this kind can be expected from string theory. For the 1695 known quotients of complete intersection manifolds by freely-acting discrete symmetries, non-freely-acting, generic symmetries arise in 381 cases and are, therefore, a relatively common feature of these manifolds. We find that 9 different discrete groups appear, ranging in group order from 2 to 18, and that both regular symmetries and R-symmetries are possible.