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

TL;DR

This paper establishes a new map relating gauge symmetry groups of heterotic strings on T^4 to other moduli space components, revealing a rank reduction mechanism involving gauge group topology, especially for non-simply-connected groups.

Contribution

It generalizes previous results for T^2 and T^3 to T^4, explicitly involving gauge group topology and providing a detailed relation to moduli space components for non-simply-connected groups.

Findings

Derived a map relating gauge groups on T^4 to moduli space components

Identified the role of gauge group topology in symmetry freezing

Validated results with extensive moduli space exploration

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.