Freezing of gauge symmetries in the heterotic string on T4

We derive a map relating the gauge symmetry groups of heterotic strings on T-4 to other components of the moduli space with rank reduction. This generalizes the results for T-2 and T-3 which mirror the singularity freezing mechanism of K3 surfaces in F and M-theory, respectively. The novel feature in six dimensions is that the map explicitly involves the topology of the gauge groups, in particular acting only on non-simply-connected ones. This relation is equivalent to that of connected components of the moduli space of flat G-bundles over T-2 with G non-simply-connected. These results are verified with a reasonably exhaustive list of gauge groups obtained with a moduli space exploration algorithm.

Automated summary

We derive a map that relates the gauge symmetry groups of heterotic strings on T-4 to other components of the moduli space with rank reduction. This relation explicitly involves the topology of the gauge groups, particularly non-simply-connected ones. The results are verified using an exhaustive list of gauge groups obtained with a moduli space exploration algorithm.