Conformal Partial Waves and the Operator Product Expansion

Details Conformal Partial Waves and the Operator Product Expansion Conformal Partial Waves and the Operator Product Expansion

2003-09-18

arxiv.org/abs/hep-th/0309180v1

Nucl.Phys. B678 (2004) 491-507

Physics

High Energy Physics

High Energy Physics - Theory

17 pages, uses harvmac

Scientific paper

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.

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