Twisted Sectors and Chern-Simons Terms in M -Theory Orbifolds

It is shown that the twisted sector spectrum, as well as the associated Chern-Simons interactions, can be determined on M -theory orbifold fixed planes that do not admit gravitational anomalies. This is demonstrated for the seven-planes arising within the context of an explicit R × S/Z2 × T /Z2 orbifold, although the results are completely general. Local anomaly cancellation in this context is shown to require fractional anomaly data that can only arise from a twisted sector on the sevenplanes, thus determining the twisted spectrum up to a small ambiguity. These results open the door to the construction of arbitrary M -theory orbifolds, including those containing fixed four-planes which are of phenomenological interest.