Minkowski Box from Yangian Bootstrap

Abstract

We extend the recently developed Yangian bootstrap for Feynman integrals to Minkowski space, focusing on the case of the one-loop box integral. The space of Yangian invariants is spanned by the Bloch-Wigner function and its discontinuities. Using only input from symmetries, we constrain the functional form of the box integral in all 64 kinematic regions up to twelve (out of a priori 256) undetermined constants. These need to be fixed by other means. We do this explicitly, employing two alternative methods. This results in a novel compact formula for the box integral valid in all kinematic regions of Minkowski space.

arXiv comment21 pages

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• Hexagonalization of Fishnet integrals I: mirror excitations
• Combinatorial Solution of the Eclectic Spin Chain
• Conformal Four-Point Integrals: Recursive Structure, Toda Equations and Double Copy
• The Feyn-Structure of Yangian Symmetry
• Hypergeometry from $\hat{\mathrm{P}}$-Symmetry: Feynman Integrals in One and Two Dimensions