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Local 4-point functions and the Knizhnik-Zamolodchikov equation. (English) Zbl 0807.35017
Sally, Paul J. jun. (ed.) et al., Mathematical aspects of conformal and topological field theories and quantum groups. AMS-IMS-SIAM summer research conference, June 13-19, 1992, Mount Holyoke College, South Hadley, MA, USA. Providence, RI: American Mathematical Society. Contemp. Math. 175, 249-267 (1994).
Summary: We classify all polynomial solutions of the Knizhnik-Zamolodchikov equation for the Möbius invariant 4-point amplitude of a primary field of the $$su_ 2$$ conformal current algebra. The exposition is based on (and reviews) recent work of Louis Michel and the authors [L. Michel, Y. S. Stanev and I. T. Todorov, Theor. Math. Phys. 92, No. 3, 1063-1074 (1992) and Teor. Mat. Fiz. 92, No. 3, 507-521 (1992)] on $${\mathcal D}_ 3$$ invariant rational 4-point functions and the local extensions of $$su_ 2$$ current algebras.
For the entire collection see [Zbl 0801.00049].
##### MSC:
 35C05 Solutions to PDEs in closed form 81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics 81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, $$W$$-algebras and other current algebras and their representations
##### Keywords:
Knizhnik-Zamolodchikov equation; polynomial solutions