Abstract
We use a moduli space exploration algorithm to produce a complete list of maximally enhanced gauge groups that are realized in the heterotic string in 7d, encompassing the usual Narain component, and five other components with rank reduction realized via nontrivial holonomy triples. Using lattice embedding techniques we find an explicit match with the mechanism of singularity freezing in M-theory on K3. The complete global data for each gauge group is explicitly given.
Highlights
The classification of gauge symmetries that can arise in the string landscape is an important problem that is comparatively easy to address for vacua with high supersymmetry
We use a moduli space exploration algorithm to produce a complete list of maximally enhanced gauge groups that are realized in the heterotic string in 7d, encompassing the usual Narain component, and five other components with rank reduction realized via nontrivial holonomy triples
G × U(1)16+d−r is realized in the heterotic string on T d as a gauge symmetry group if and only if its weight lattice M admit√s a primitive embedding in the Narain lattice II16+d,d such that the vectors in M of length 2 are roots
Summary
We see that the lattice alone is not sufficient to determine the allowed gauge groups, but rather one must impose a constraint in the embeddings characterized by an integer, which comes from the string theory but is ad hoc from the point of view of the lattice (see Proposition 3.3) Implementing this constraint in our algorithm we obtain a list of maximally enhanced gauge algebras for each component. It is natural to ask how this mechanism of partial freezing appears in the heterotic string We study this problem by exploiting relations between the reduced rank momentum lattices and the Narain lattice and find a match with the known results in the M-theory side. In appendix A we leave some comments regarding the role of some technicalities of lattice embeddings in the heterotic string, which may help the reader who is not used to thinking in these terms
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