The chiral-part conjecture for heterotic/type I duality

Let $X$ be a Calabi\Yau $5$-fold. The type I topological string on $X$ is the unoriented topological $B$-model with its open-string sector, whose gauge theory has structure group ${\rm SO}(32)$. The chiral-part conjecture. The appropriate part of the heterotic string is the chiral part, and there is an equivalence between the type I topological string on $X$ and the chiral part of the ${\rm SO}(32)$ heterotic string with target $X$. This is the proposed topological counterpart of the expected duality between the physical type I and heterotic strings; the text notes that defining the chiral heterotic string at loop level requires suitable integration cycles and leaves that issue for future work.