Conformal Four Point Functions and the Operator Product Expansion

Abstract

Various aspects of the four point function for scalar fields in conformally invariant theories are analysed. This depends on an arbitrary function of two conformal invariants u,v. A recurrence relation for the function corresponding to the contribution of an arbitrary spin field in the operator product expansion to the four point function is derived. This is solved explicitly in two and four dimensions in terms of ordinary hypergeometric functions of variables z,x which are simply related to u,v. The operator product expansion analysis is applied to the explicit expressions for the four point function found for free scalar, fermion and vector field theories in four dimensions. The results for four point functions obtained by using the AdS/CFT correspondence are also analysed in terms of functions related to those appearing in the operator product discussion.

38 pages, plain TeX file using harvmac; revised version minor changes and an extra reference, revised version2, further corrections

References in corpus (8)

• Operator Product Expansion of the Lowest Weight CPOs in N=4 SYM_4 at Strong Coupling
• The Operator Product Expansion of N=4 SYM and the 4-point Functions of Supergravity
• Four-point Functions of Lowest Weight CPOs in N=4 SYM_4 in Supergravity Approximation
• Implications of N=1 Superconformal Symmetry for Chiral Fields
• Four-point functions in N=2 superconformal field theories
• A note on the analyticity of AdS scalar exchange graphs in the crossed channel
• AdS Box Graphs, Unitarity and Operator Product Expansions
• OPEs and 4-point Functions in AdS/CFT Correspondence

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