Gauge group topology of 8D Chaudhuri-Hockney-Lykken vacua
Mirjam Cvetič, Markus Dierigl, Ling Lin, Hao Y. Zhang
Abstract
Compactifications of the Chaudhuri-Hockney-Lykken (CHL) string to eight dimensions can be characterized by embeddings of root lattices into the rank 12 momentum lattice ${\mathrm{\ensuremath{\Lambda}}}_{M}$, the so-called Mikhailov lattice. Based on these 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 nontrivial ${\ensuremath{\pi}}_{1}(G)\ensuremath{\equiv}\mathcal{Z}$ for the non-Abelian gauge group $G$ as having gauged a $\mathcal{Z}$ 1-form symmetry, we also prove that all CHL gauge groups are free of a certain anomaly [1] that would obstruct this gauging. We verify this by explicitly computing $\mathcal{Z}$ for all 8D CHL vacua with $\mathrm{rank}(G)=10$. 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.