Anomaly cancellation in M-theory on orbifolds Original Research Article

We present calculation of the anomaly cancellation in M-theory on orbifolds S1/Z2 and T5/Z2 in the upstairs approach. The main requirement that allows one to uniquely define solutions to the modified Bianchi identities in this case is that the field strength G be globally defined on S1 or T5 and properly transforming under Z2. We solve for general G that satisfies these requirements and explicitly construct anomaly-free theories in the upstairs approach. We also obtain the solutions in the presence of five-branes. All these constructions show equivalence of the downstairs and upstairs approaches. For example in the S1/Z2 case the ten-dimensional gauge coupling and the anomaly cancellation at each wall are the same as in the downstairs approach.