Intersecting Orbifold Planes and Local Anomaly Cancellation in M-Theory

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A systematic program is developed for analyzing and cancelling local anomalies on networks of intersecting orbifold planes in the context of M-theory. Through a delicate balance of factors, it is discovered that local anomaly matching on the lower-dimensional intersection of two orbifold planes may require twisted matter on those planes which do not conventionally support an anomaly (such as odd-dimensional planes). In this way, gravitational anomalies can, in principle, tell us about (twisted) gauge groups on subspaces which are not necessarily ten-, six- or two-dimensional. An example is worked out for the case of an S¹/ Z₂× T⁴/ Z₂ orbifold and possible implications for four-dimensional physics are speculated on.