M-theory on S-1/Z(2): new facts from a careful analysis

We carefully reexamine the issues of solving the modified Bianchi identity, anomaly cancellations and flux quantization in the S-1/Z(2) orbifold of M- theory using the boundary-free "upstairs" formalism, avoiding several misco nceptions present in earlier literature. While the solution for the four-fo rm G to the modified Bianchi identity appears to depend on an arbitrary par ameter b, we show that requiring G to be globally well-defined, i.e., invar iant under small and large gauge and local Lorentz transformations, fixes b = i. This value also is necessary for a consistent reduction to the hetero tic string in the small-radius limit. Insisting on properly defining all fi elds on the circle, we find that there is a previously unnoticed additional contribution to the anomaly inflow from the eleven-dimensional topological term. Anomaly cancellation then requires a quadratic relation between b an d the combination lambda(6)/kappa(4) of the gauge and gravitational couplin g constants lambda and kappa. This contrasts with previous beliefs that ano maly cancellation would give a cubic equation for b. We observe that our so lution for G automatically satisfies integer or half-integer flux quantizat ion for the appropriate cycles. We explicitly write out the anomaly cancell ing terms of the heterotic string as inherited from the M-theory approach. They differ from the usual ones by the addition of a well-defined local cou nterterm. We also show how five-branes enter our analysis. (C) 2000 Elsevie r Science B.V. All rights reserved.