Abstract
The author calculates the gauge, gravitational and mixed (perturbative) anomalies in general six-dimensional Kaluza-Klein theories, including supergravity models, from the Atiyah-Singer index theorems and discuss the conditions for anomaly cancellation. The topological meaning of the index polynomials, when used in computing anomalies, is emphasised. The absence of anomalies in the compactified heterotic superstring theory in six dimensions is reviewed. The existence of matter and gauge coupled anomaly-free U(1)-gauged six-dimensional supergravities with E8(X)E7, E8(X)E6(X)SU(2), E7(X)E6(X)SU(2)(X)U(1), E7(X)E7 and E6(X)E6(X) SU(2)(X)SU(2)(X)U(1) gauge groups is proved without any reference to the compactification procedure. It realises a highly non-trivial check of the anomaly cancellation in some K3 compactified heterotic superstrings. Some comments on global anomalies in six dimensions are made.
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