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تسجيل مستخدم جديدOn the Gauge Group Topology of 8d CHL Vacua
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Compactifications of the CHL string to eight dimensions can be characterized by embeddings of root lattices into the rank 12 momentum lattice $Lambda_M$, the so-called Mikhailov lattice. Based on this data, we devise a method to determine the global gauge group structure including all $U(1)$ factors. The key observation is that, while the physical states correspond to vectors in the momentum lattice, the gauge group topology is encoded in its dual. Interpreting a non-trivial $pi_1(G) equiv {cal Z}$ for the non-Abelian gauge group $G$ as having gauged a ${cal Z}$ 1-form symmetry, we also prove that all CHL gauge groups are free of a certain anomaly (arXiv:2008.10605) that would obstruct this gauging. We verify this by explicitly computing ${cal Z}$ for all 8d CHL vacua with rank$(G)=10$. Since our method applies also to $T^2$ compactifications of heterotic strings, we further establish a map that determines any CHL gauge group topology from that of a parent heterotic model.
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