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Solving the conformal constraints for scalar operators in momentum space and the evaluation of Feynman’s master integrals

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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 hyper-geometric 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.

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Authors and Affiliations

  1. Dipartimento di Matematica e Fisica “Ennio De Giorgi”, Università del Salento and INFN, Lecce, Via Arnesano, 73100, Lecce, Italy

    Claudio Corianò, Luigi Delle Rose & Mirko Serino

  2. Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, U.S.A.

    Emil Mottola

Authors
  1. Claudio Corianò
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  2. Luigi Delle Rose
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  3. Emil Mottola
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  4. Mirko Serino
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Correspondence to Claudio Corianò.

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ArXiv ePrint: 1304.6944

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Corianò, C., Rose, L.D., Mottola, E. et al. Solving the conformal constraints for scalar operators in momentum space and the evaluation of Feynman’s master integrals. J. High Energ. Phys. 2013, 11 (2013). https://doi.org/10.1007/JHEP07(2013)011

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  • DOI: https://doi.org/10.1007/JHEP07(2013)011

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