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Graphical functions and single-valued multiple polylogarithms
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Graphical functions are single-valued complex functions which arise from Feynman amplitudes. We study their properties and use their connection to multiple polylogarithms to calculate Feynman periods. For the zig-zag and two more families of phi^4 periods we give exact results modulo products. These periods are proved to be expressible as integer linear combinations of single-valued multiple polylogarithms evaluated at one. For the larger family of 'constructible' graphs we give an algorithm that allows one to calculate their periods by computer algebra. The theory of graphical functions is used to prove the zig-zag conjecture.
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Forward citations
Cited by 3 Pith papers
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OPE-based recursive renormalization for mixed composite operators gives five-loop anomalous dimensions in phi^4 and two-loop in phi^3 models.
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Four-loop anomalous dimension of φ^Q in scalar-QED computed via OPE, extending prior three-loop results and validating the method in a gauge theory.
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Graphical Functions by Examples
Graphical functions, defined as massless three-point position-space integrals, serve as a powerful tool for evaluating multi-loop Feynman integrals, with extensions to conformal field theory and recent algorithmic com...
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