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M-Theory, type IIA superstrings, and elliptic cohomology. (English) Zbl 1082.81070

Summary: The topological part of the M-theory partition function was shown by Witten to be encoded in the index of an \(E_8\) bundle in eleven dimensions. This partition function is, however, not automatically anomalyfree. We observe here that the vanishing \(W_7 = 0\) of the Diaconescu-Moore-Witten anomaly in IIA and compactified M-theory partition function is equivalent to orientability of spacetime with respect to (complex-oriented) elliptic cohomology. Motivated by this, we define an elliptic cohomology correction to the IIA partition function, and propose its relationship to interaction between 2- and 5-branes in the M-theory limit.

MSC:

81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
83E15 Kaluza-Klein and other higher-dimensional theories
83E30 String and superstring theories in gravitational theory
81T50 Anomalies in quantum field theory
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