Generalized Green-Schwarz anomaly cancellation mechanism

We show that the chiral anomaly can be canceled by a single antisymmetric tensor if the anomaly form factorizes into the product of two invariant polynomials of curvature two-forms, R and F. This generalizes the Green-Schwarz cancellation mechanism, where the factorization is of the form (Tr$R^2$-Tr$F^2$) times an invariant polynomial. The Yang-Mills group constraints differ from those obtained by the Green-Schwarz mechanism if the anomaly form is factorized differently and thus new anomaly-free theories emerge. This generalized mechanism works for any theories in D=4k dimensions and nonsupergravity theories in D=4k-2. However, for supergravity-type theories in D=4k-2 only the original Green-Schwarz factorization works. We explicitly construct many anomaly-free theories in D=8 and D=10, using the generalized mechanism.