Conformal partial waves in momentum space

The decomposition of 4-point correlation functions into conformal partial waves is a central tool in the study of conformal field theory. We compute these partial waves for scalar operators in Minkowski momentum space, and find a closed-form result valid in arbitrary space-time dimension d ? 3 (including non-integer d). Each conformal partial wave is expressed as a sum over ordinary spin partial waves, and the coefficients of this sum factorize into a product of vertex functions that only depend on the conformal data of the incoming, respectively outgoing operators. As a simple example, we apply this conformal partial wave decomposition to the scalar box integral in d = 4 dimensions.

Automated summary

The decomposition of 4-point correlation functions into conformal partial waves is a key tool in the study of conformal field theory. By computing scalar operator partial waves in Minkowski momentum space, a closed-form result valid in arbitrary space-time dimensions is obtained. Each conformal partial wave is expressed as a sum over ordinary spin partial waves, with coefficients that factorize into products of vertex functions dependent only on the conformal data of the incoming or outgoing operators.