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Hořava-Witten theory on ${\mathbf{S}}^1\vee{\mathbf{S}}^1$ as type 0 orientifold
We investigate dualities between ${\mathbf{Z}}_2$ quotients of recently proposed compactifications of M-theory on `quantum geometries' of the form ${\mathbf{S}}^1\vee{\mathbf{S}}^1$ and 10d orientifolds of type 0A and 0B string theories. In particular, we relate the Hořava-Witten theory on ${\mathbf
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