Freezing of gauge symmetries in the heterotic string on T4

Abstract

We derive a map relating the gauge symmetry groups of heterotic strings on T4 to other components of the moduli space with rank reduction. This generalizes the results for T2 and T3 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 T2 with G non-simply-connected. These results are verified with a reasonably exhaustive list of gauge groups obtained with a moduli space exploration algorithm.