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Abstract
We complete the proof of “Feynman rules” for constructing M-point conformal blocks with external and internal scalars in any topology for arbitrary M in any spacetime dimension by combining the rules for the blocks (based on their Witten diagram interpretation) with the rules for the construction of conformal cross ratios (based on the OPE and “flow diagrams”). The full set of Feynman rules leads to blocks as power series of the hypergeometric type in the conformal cross ratios. We then provide a proof by recursion of the Feynman rules which relies heavily on the first Barnes lemma and the decomposition of the topology of interest in comb structures. Finally, we provide a nine-point example to illustrate the rules.
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1 Université Laval, Département de Physique, de Génie Physique et d’Optique, Québec, Canada (GRID:grid.23856.3a) (ISNI:0000 0004 1936 8390)
2 Pomona College, Department of Physics and Astronomy, Claremont, USA (GRID:grid.262007.1) (ISNI:0000 0001 2161 0463)
3 Beijing Institute of Mathematical Sciences and Applications (BIMSA), Beijing, P. R. China (GRID:grid.262007.1); Tsinghua University, Yau Mathematical Sciences Center, Beijing, China (GRID:grid.12527.33) (ISNI:0000 0001 0662 3178)
4 California Institute of Technology, Division of Physics, Mathematics and Astronomy, Pasadena, USA (GRID:grid.20861.3d) (ISNI:0000000107068890); Department of Physics, Indian Institute of Technology Delhi, New Delhi, India (GRID:grid.417967.a) (ISNI:0000 0004 0558 8755)
5 Yale University, Department of Physics, New Haven, USA (GRID:grid.47100.32) (ISNI:0000000419368710)