Determinants, torsion, and strings. (English) Zbl 0606.58013
In quantum field theory the anomalies are usually viewed as arising from the nontrivial topology (over the reals) of the determinant line bundle \({\mathcal L}\) of a Dirac operator. The present paper investigates the geometrical origin of the anomalies. The paper starts with a review of the construction of a metric and a connection on h, and the evaluation of its curvature and its holonomy. It proceeds with the interpretation of the conformal anomaly of the bosonic string in terms of the geometry - but not merely the topology - of the determinant line bundle. In addition, the relationship between the torsion of h and the global anomalies is investigated, certain torsion invariants in cohomoloy are constructed, their effect on the anomalies in the heterotic string are established, and sufficient conditions for the cancellation of global anomalies are obtained.
Reviewer: B.Xanthopoulos
MSC:
| 58D30 | Applications of manifolds of mappings to the sciences |
| 81T99 | Quantum field theory; related classical field theories |
| 53C80 | Applications of global differential geometry to the sciences |
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