Freezing of Gauge Symmetries in the Heterotic String on $T^4$

Understand

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.