Anomalies in super p-branes

The Green-Schwarz action for the superstring may be generalised to the case of extended objects of p spatial dimensions. It is known for the superstring that only the ten-dimensional theory is consistent at the quantum level. In the light-cone quantisation that we use, consistency of the theory is tested by the closure of the spacetime Lorentz and supersymmetry algebras. For the higher-dimensional super p-branes, the corresponding analysis is much more complicated, owing to the intrinsic non-linearity of the theories. However, certain consistency checks are possible, based on the fact that the degeneracies of the states of the theories should be compatible with the appropriate little groups for massless and massive modes. We apply such counting tests to the twelve super p-branes and conclude that all, except for the ten-dimensional super-string and the eleven-dimensional supermembrane, are quantum mechanically inconsistent. The eleven-dimensional case passes all the tests that we could perform. (author)