Gluing Ladders into Fishnets

Abstract

We use integrability at weak coupling to compute fishnet diagrams for four-point correlation functions in planar ${\varphi }^4$ theory. The results are always multi-linear combinations of ladder integrals, which are in turn built out of classical polylogarithms. The Steinmann relations provide a powerful constraint on such linear combinations, leading to a natural conjecture for any fishnet diagram as the determinant of a matrix of ladder integrals.

6 pages, 4 figures; v2, minor corrrections, e.g. in fig. 2 caption

References in corpus (8)

• Comments on operators with large spin
• Bootstrapping a Five-Loop Amplitude Using Steinmann Relations
• An Operator Product Expansion for Polygonal null Wilson Loops
• BFKL Pomeron, Reggeized gluons and Bern-Dixon-Smirnov amplitudes
• Heptagons from the Steinmann Cluster Bootstrap
• Hexagonalization of Correlation Functions
• Exponential suppression with four legs and an infinity of loops
• Evaluating four-loop conformal Feynman integrals by D-dimensional differential equations

Cited by in corpus (72)

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• Bi-scalar integrable CFT at any dimension
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• Sequential Discontinuities of Feynman Integrals and the Monodromy Group
• Exact Correlation Functions in Conformal Fishnet Theory
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• Numerical Loop-Tree Duality: contour deformation and subtraction
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• The Octagon as a Determinant
• Continuum limit of fishnet graphs and AdS sigma model
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• Integrability for Feynman Integrals
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• Minkowski Box from Yangian Bootstrap
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