Yangian Bootstrap for Conformal Feynman Integrals

Abstract

We explore the idea to bootstrap Feynman integrals using integrability. In particular, we put the recently discovered Yangian symmetry of conformal Feynman integrals to work. As a prototypical example we demonstrate that the D-dimensional box integral with generic propagator powers is completely fixed by its symmetries to be a particular linear combination of Appell hypergeometric functions. In this context the Bloch-Wigner function arises as a special Yangian invariant in 4D. The bootstrap procedure for the box integral is naturally structured in algorithmic form. We then discuss the Yangian constraints for the six-point double box integral as well as for the related hexagon. For the latter we argue that the constraints are solved by a set of generalized Lauricella functions and we comment on complications in identifying the integral as a certain linear combination of these. Finally, we elaborate on the close relation to the Mellin-Barnes technique and argue that it generates Yangian invariants as sums of residues.

arXiv comment20 pages, v2: minor improvements

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• FeynGKZ: a Mathematica package for solving Feynman integrals using GKZ hypergeometric systems
• Massive Conformal Symmetry and Integrability for Feynman Integrals
• The elliptic double box and symbology beyond polylogarithms
• All-Mass $n$-gon Integrals in $n$ Dimensions
• Three-Body Effective Potential in General Relativity at Second Post-Minkowskian Order and Resulting Post-Newtonian Contributions
• The Double Box and Hexagon Conformal Feynman Integrals
• Yangian Bootstrap for Massive Feynman Integrals
• The Wilson-loop $d\log$ representation for Feynman integrals
• Massive Fishnets
• The Loom for General Fishnet CFTs
• Conformal Correlation functions in four dimensions from Quaternionic Lauricella system
• Massive One-loop Conformal Feynman Integrals and Quadratic Transformations of Multiple Hypergeometric Series
• Recursive computation of Feynman periods
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• Integrability for Feynman Integrals
• The Dual Conformal Box Integral in Minkowski Space
• Minkowski Box from Yangian Bootstrap
• Yangian Symmetry in Holographic Correlators
• Hexagonalization of Fishnet integrals I: mirror excitations
• Multiple Mellin-Barnes integrals with straight contours
• Combinatorial Solution of the Eclectic Spin Chain
• Conformal Four-Point Integrals: Recursive Structure, Toda Equations and Double Copy
• Amplitudes in fishnet theories in diverse dimensions and Box ladder diagrams
• Feynman Integrals of Grassmannians
• GKZ-system of the 2-loop self energy with 4 propagators
• GKZ hypergeometric systems of the three-loop vacuum Feynman integrals
• The Feyn-Structure of Yangian Symmetry
• A Large Twist Limit for Any Operator
• Non-Local Symmetries of Planar Feynman Integrals
• Hypergeometry from $\hat{\mathrm{P}}$-Symmetry: Feynman Integrals in One and Two Dimensions