Freezing of gauge symmetries in the heterotic string on T 4

Abstract 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.