Ho\v{r}ava-Witten 理论在 ${\mathbf{S}}^1\vee{\mathbf{S}}^1$ 上的 type 0 定向轨道

我们研究 ${\mathbf{Z}}_2$ 商的 M 理论在 `量子几何' 形式为 ${\mathbf{S}}^1\vee{\mathbf{S}}^1$ 的紧凑化置于 10 维 type 0A 和 0B 字符串理论定向轨道之间的对偶性。在 particular, we 将 Ho\v{r}ava-Witten 理论 on ${\mathbf{S}}^1\vee{\mathbf{S}}^1$ 关联到具有 $SO(16)^4$ 规范群的 0B 定向轨道。 resulting dictionary 提供了几何解释，以解释 0B 定向轨道的特征特征，如规范群的翻倍, while the perturbative spectrum of the 0B orientifold indicates the emergence of novel M-theoretic degrees of freedom associated with the junction point. The 0B orientifold further reveals the existence of two variants of the theory on ${\mathbf{S}}^1\vee{\mathbf{S}}^1$, corresponding to equal vs opposite (i.e., standard vs Fabinger-Ho\v{r}ava) orientations of the $E_8$ walls. We also analyze additional 0A and 0B orientifolds whose open string sectors do not arise from higher-dimensional gauge fields in M-theory and whose microscopic interpretation remains an open problem.