Anomaly cancellation in M - theory

We show the complete cancellation of gauge and gravitational anomalies in the Mtheory of Horava and Witten using their boundary contribution, and a term coming from the existence of two and five-branes. A factor of three discrepancy noted in an earlier work is resolved. We end with a comment on flux quantization. e-mail: [email protected] In the M-theory of Horava and Witten [1] several consistency checks associated with anomaly cancellation were verified. However one test which involved a numerical coefficient of a purely gravitational anomaly was not carried out. In an earlier paper by the author [2] the coefficient of a certain M-theory Green-Schwarz term [3] was determined, but there appeared to be a factor of three discrepancy with the expression (3.12) of [1]. In this short note we review the anomaly cancellation argument and find that the M-theory topological terms do indeed cancel both gauge and gravitational anomalies. Finally we comment on flux quantization in M-theory in the light of a recent paper by E. Witten[4]. We work with the “downstairs” version of the theory, i.e. on an 11-D manifold M = M10 × S/Z2. The topological term in the low energy effective action of M-theory is