Gravitational Anomaly Cancellation for M -Theory Fivebranes

We study gravitational anomalies for fivebranes in M theory. We show that an apparent anomaly in diffeomorphisms acting on the normal bundle is cancelled by a careful treatment of the M theory Chern-Simons coupling in the presence of fivebranes. One interesting aspect of our treatment is the way in which a magnetic object (the fivebrane) is smoothed out through coupling to gravity and the resulting relation between antisymmetric tensor gauge transformations and diffeomorphisms in the presence of a fivebrane. March 25, 1998 1 School of Mathematics, Institute for Advanced Study, Olden Lane, Princeton, NJ 08540, permanent address: Dept. of Mathematics, University of Texas, Austin, TX 78712 2 Enrico Fermi Institute, 5640 Ellis Avenue, University of Chicago, Chicago, IL 60637 3 Department of Physics, Yale University, New Haven, CT 06520