Worldvolume 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 worldvolume 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 1/2 of that required by the string/fivebrane duality conjecture. As a consequence the worldvolume anomaly vanishes if the heterotic fields consist of 16 (rather than 32) complex Weyl fermions on the worldvolume. 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. European Community Programme Gauge Theories, Applied Supersymmetry and Quantum Gravity " with a financial contribution under SC1–CT–92–D789.