Interactions as intertwiners in 4D QFT

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Regular Article - Theoretical Physics


In a recent paper we showed that the correlators of free scalar field theory in four dimensions can be constructed from a two dimensional topological field theory based on so(4, 2) equivariant maps (intertwiners). The free field result, along with recent results of Frenkel and Libine on equivariance properties of Feynman integrals, are developed further in this paper. We show that the coefficient of the log term in the 1-loop 4-point conformal integral is a projector in the tensor product of so(4, 2) representations. We also show that the 1-loop 4-point integral can be written as a sum of four terms, each associated with the quantum equation of motion for one of the four external legs. The quantum equation of motion is shown to be related to equivariant maps involving indecomposable representations of so(4, 2), a phenomenon which illuminates multiplet recombination. The harmonic expansion method for Feynman integrals is a powerful tool for arriving at these results. The generalization to other interactions and higher loops is discussed.


AdS-CFT Correspondence Conformal and W Symmetry Duality in Gauge Field Theories Gauge-gravity correspondence 


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This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.


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© The Author(s) 2016

Authors and Affiliations

  1. 1.National Institute for Theoretical Physics, School of Physics and Mandelstam Institute for Theoretical PhysicsUniversity of WitwatersrandWitsSouth Africa
  2. 2.Centre for Research in String Theory, School of Physics and AstronomyQueen Mary University of LondonLondonU.K.

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