Free field approach to 2-dimensional conformal field theories. (English) Zbl 0784.17041
Eguchi, T. (ed.) et al., Common trends in mathematics and quantum field theories. 1990 Yukawa international seminar school: Kansai Seminar House, Kyoto, Japan, May 10-16, 1990. Workshop: RIMS, Kyoto University, Japan, May 17-19, 1990. Tokyo: Yukawa Institute for Theoretical Physics, Prog. Theor. Phys., Suppl. 102, 67-135 (1990).
Summary: We review various aspects of the free field approach to (rational) conformal field theories. In particular, we discuss resolutions of irreducible modules in terms of free field Fock spaces for WZNW-models and their coset models, as well as the free field realization of chiral vertex operators. We provide a host of clarifying examples and detailed proofs of results that were announced elsewhere.
For the entire collection see [Zbl 0777.00029].
For the entire collection see [Zbl 0777.00029].
MSC:
| 17B81 | Applications of Lie (super)algebras to physics, etc. |
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
Keywords:
affine Kac-Moody algebras; resolutions of irreducible modules; free field Fock spaces; WZNW-models; chiral vertex operatorsReferences:
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