Solving the conformal constraints for scalar operators in momentum space and the evaluation of feynman's master integrals
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Publication:737366
DOI10.1007/JHEP07(2013)011zbMATH Open1342.81138arXiv1304.6944OpenAlexW1989379892MaRDI QIDQ737366
Author name not available (Why is that?)
Publication date: 12 August 2016
Published in: (Search for Journal in Brave)
Abstract: We investigate the structure of the constraints on three-point correlation functions emerging when conformal invariance is imposed in momentum space and in arbitrary space-time dimensions, presenting a derivation of their solutions for arbitrary scalar operators. We show that the differential equations generated by the requirement of symmetry under special conformal transformations coincide with those satisfied by generalized hypergeometric functions (Appell's functions). Combined with the position space expression of this correlator, whose Fourier transform is given by a family of generalized Feynman (master) integrals, the method allows to derive the expression of such integrals in a completely independent way, bypassing the use of Mellin-Barnes techniques, which have been used in the past. The application of the special conformal constraints generates a new recursion relation for this family of integrals.
Full work available at URL: https://arxiv.org/abs/1304.6944
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