For locally symmetric moduli spaces satisfying a compactifiability constraint, every infinite-distance limit produces an exponentially light tower of states, with decay rates forming the convex hull of the weights of a representation of the isometry group.
Freezing of Gauge Symmetries in the Heterotic String on $T^4$
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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.
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The Boundary of Symmetric Moduli Spaces and the Swampland Distance Conjecture
For locally symmetric moduli spaces satisfying a compactifiability constraint, every infinite-distance limit produces an exponentially light tower of states, with decay rates forming the convex hull of the weights of a representation of the isometry group.