World-volume and target-space anomalies in the D = 10 super-fivebrane sigma model

The fields of the conjectured “heterotic” super-fivebrane sigma model in ten dimensions are made out of a well-known gravitational sector, the X and the ϑ, and of a still unknown heterotic sector which should be coupled to the Yang-Mills fields. We compute the one-loop d = 6 world-volume and D = 10 target-space Lorentz anomalies which arise from the gravitational sector of the heterotic super-fivebrane sigma model, using a method which we developed previously for the Green-Schwarz heterotic superstring. These anomalies turn out to carry an overall coefficient which is half of that required by the string-fivebrane duality conjecture. As a consequence, the world-volume anomaly vanishes if the heterotic fields consist of 16 (rather than 32) complex Weyl fermions on the world-volume. This implies that the string-fivebrane duality conjecture can not be based on a “heterotic” super-fivebrane sigma model with only fermions in the heterotic sector. Possible implications of this result are discussed.