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Global gravitational anomalies. (English) Zbl 0581.58038

Anomalies in field theories can destroy the consistency of quantum field theory. Cancellation of perturbative anomalies can be betraced to the invariance of the effective action under gauge and coordinate transformations that can be reached continuously from the identity. The author discusses more general transformations that cannot be reached from the identity in a continuous way. Lack of invariance of the effective action under these transformations causes global anomaly. Several specific and general methods are developed and applied to examine global anomalies in present supergravity theories. For the O(32) and \(E_ 8\times E_ 8\) theory it is shown that they have no global anomalies in ten dimensions. It is pointed out and demonstrated that global anomalies may put restrictions on compactifications of these theories.
Reviewer: P.Kramer

MSC:

58J90 Applications of PDEs on manifolds
81T08 Constructive quantum field theory
83E50 Supergravity
81T60 Supersymmetric field theories in quantum mechanics
83C45 Quantization of the gravitational field
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