×

Global anomalies in string theory. (English) Zbl 0643.53071

Anomalies, geometry, topology, Symp. Chicago/Ill. 1985, 61-99 (1985).
Summary: [For the entire collection see Zbl 0637.00005.]
Various questions involving global anomalies in particle theory and string theory are addressed. It is shown that the question of whether a manifold is a spin manifold is equivalent to a question about global anomalies in the propagation of a point particle. In the superstring case, it is shown that the measure of the heterotic theory has no global anomalies on any Riemann surface. This generalizes known one loop results. Also, a topological condition is derived which restricts the possible choices of Wilson lines for grand unified symmetry breaking. It is argued that the long-term development of global anomalies in string theory will involve eventual study of global anomalies in the determinant of the Dirac-Ramond operator.

MSC:

53C80 Applications of global differential geometry to the sciences
57R99 Differential topology
81T60 Supersymmetric field theories in quantum mechanics

Citations:

Zbl 0637.00005