Closed and open conformal field theories and their anomalies. (English) Zbl 1091.81073
Summary: We describe a formalism allowing a completely mathematical rigorous approach to closed and open conformal field theories with general anomaly. We also propose a way of formalizing modular functors with positive and negative parts, and outline some connections with other topics, in particular elliptic cohomology.
MSC:
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
| 81T50 | Anomalies in quantum field theory |
| 46M20 | Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.) |
| 58J22 | Exotic index theories on manifolds |
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