A surprising anomaly in diffeomorphisms acting on the normal bundle of the M-theory fivebrane remained a puzzle for almost two years. We present a cancellation mechanism based on a careful treatment of the fivebrane by smoothing it out through coupling to gravity which results in a relation between antisymmetric tensor gauge transformations and diffeomorphisms and leads to a complete cancellation of the anomalies. This formalism is used for derivation of the R-symmetry anomalies of the AN (0,2) tensor-multiplet theories and for understanding the role of anomalies in the AdS/CFT correspondence. The Kaluza-Klein origin of Chern-Simons terms in lower-dimensional supergravity theories is displayed via modification of the Freund-Rubin ansatz. The results imply the existence of interesting 1/N corrections in the AdS/CFT correspondence. A simple derivation of black hole entropy in d=4, N=2 compactifications of M-theory is presented.
We discuss aspects of the renormalization group flow of quiver gauge theories in two dimensions, with little or no supersymmetry, in the spirit of earlier work of Zamolodchikov on non-supersymmetric Landau-Ginzburg theory. By using a variety of techniques including analysis of chiral symmetries, identification of operators, and analysis of perturbative gauge theory diagrams, we show that these theories can (at least) be fine-tuned to flow to orbifold conformal field theory in the infrared. This provides a linear sigma model description of string backgrounds with no spacetime supersymmetry, whose applications and limitations we begin to explore.