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.

27 pages, v2: minor corrections

References in corpus (5)

• Mordell-Weil Torsion and the Global Structure of Gauge Groups in F-theory
• Compactness of Brane Moduli and the String Lamppost Principle in $d>6$
• Exploring the landscape of CHL strings on T^d
• Symmetry Enhancements in 7d Heterotic Strings
• On the Gauge Group Topology of 8d CHL Vacua

Cited by in corpus (5)

• Compactness of Brane Moduli and the String Lamppost Principle in $d>6$
• One Loop to Rule Them All: Eight and Nine Dimensional String Vacua from Junctions
• Unifying the 6D $\mathcal{N}=(1,1)$ String Landscape
• New Supersymmetric String Moduli Spaces from Frozen Singularities
• Flat equivariant gerbes: holonomies and dualities