Heterotic and type I strings from twisted supermembranes

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As shown by Hořava and Witten, there are gravitational anomalies at the boundaries of M¹⁰× S¹/Z₂ of 11 dimensional supergravity. They showed that only 10 dimensional vector multiplets belonging to E₈ gauge group can be consistently coupled to this theory. Thus, the dimensional reduction of this theory should be the low energy limit of the E₈× E₈ heterotic string. Here we assume that M-theory is a theory of supermembranes which includes twisted supermembranes. We show that for a target space M¹⁰× S¹/Z₂, in the limit in which S¹/Z₂ is small, the effective action is the E₈× E₈ heterotic string. We also consider supermembranes on M⁹× S¹× S¹/Z₂ and find the dualities expected from 11 dimensional supergravity on this manifold. We show that the requirements for worldsheet anomaly cancellations at the boundaries of the worldvolume action are the same requirements imposed on the Hořava-Witten action.