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.
Highlights
The quintic in P4 has a complex structure moduli space of dimension 101 and a freely-acting Z5×Z5 symmetry which appears only at a 5-dimensional sub-locus on this moduli space. This seems to suggest that discrete symmetries in four-dimensional string models, at least insofar as they originate from symmetries of the compactification manifold, are typically quite non-generic and are unlikely to play a major role in phenomenology
The data for both the CICY manifolds and the freely-acting symmetries is available for download and we will use the version of this dataset available at [29]
An entry in this dataset consists of a pair, (X, Gf. Clearly NG (Gf)), of a CICY manifold and a freely-acting symmetry
Summary
The quintic in P4 has a complex structure moduli space of dimension 101 and a freely-acting Z5×Z5 symmetry which appears only at a 5-dimensional sub-locus on this moduli space This seems to suggest that discrete symmetries in four-dimensional string models, at least insofar as they originate from symmetries of the compactification manifold, are typically quite non-generic and are unlikely to play a major role in phenomenology. One of the main points of the present paper is that this statement does not apply to certain classes of CY manifolds This means that, contrary to expectation, low-energy symmetries which descend from these manifolds can be generic and phenomenologically relevant
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