Anomalies in super p-branes

Publisher Website
Google Scholar
Abstract
The Green-Schwarz action for the superstring may be generalised to the case of extended objects of p spatial dimensions. Twelve such super p-branes exist classically, including the superstring in ten, six, four and three spacetime 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 the authors 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. The authors apply such counting tests to the twelve super p-branes and conclude that all, except for the ten-dimensional superstring and the eleven-dimensional supermembrane, are quantum mechanically inconsistent. The eleven-dimensional case passes all the tests that they could perform. Further analysis is required in order to settle whether this remaining case is consistent.

This publication has 5 references indexed in Scilit: