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Conformal partial waves and the operator product expansion. (English) Zbl 1097.81735
Summary: By solving the two variable differential equations which arise from finding the eigenfunctions for the Casimir operator for $$O(d,2)$$ succinct expressions are found for the functions, conformal partial waves, representing the contribution of an operator of arbitrary scale dimension $$\Delta$$ and spin $$\ell$$ together with its descendants to conformal four point functions for $$d=4$$, recovering old results, and also for $$d=6$$. The results are expressed in terms of ordinary hypergeometric functions of variables $$x,z$$ which are simply related to the usual conformal invariants. An expression for the conformal partial wave amplitude valid for any dimension is also found in terms of a sum over two variable symmetric Jack polynomials which is used to derive relations for the conformal partial waves.

##### MSC:
 81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics 33C90 Applications of hypergeometric functions
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##### References:
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