Bootstrapping elliptic Feynman integrals using Schubert analysis

Abstract

The symbol bootstrap has proven to be a powerful tool for calculating polylogarithmic Feynman integrals and scattering amplitudes. In this letter, we initiate the symbol bootstrap for elliptic Feynman integrals. Concretely, we bootstrap the symbol of the twelve-point two-loop double-box integral in four dimensions, which depends on nine dual-conformal cross ratios. We obtain the symbol alphabet, which contains 100 logarithms as well as 9 simple elliptic integrals, via a Schubert-type analysis, which we equally generalize to the elliptic case. In particular, we find a compact, one-line formula for the (2,2)-coproduct of the result.

5+6 pages, 4 figures

References in corpus (26)

• Classical Polylogarithms for Amplitudes and Wilson Loops
• Bootstrapping a Five-Loop Amplitude Using Steinmann Relations
• Bootstrapping an NMHV amplitude through three loops
• The two-loop sunrise graph in two space-time dimensions with arbitrary masses in terms of elliptic dilogarithms
• The kite integral to all orders in terms of elliptic polylogarithms
• Bootstrapping the QCD soft anomalous dimension
• Elliptic polylogarithms and Feynman parameter integrals
• New differential equations for on-shell loop integrals
• Cluster algebras for Feynman integrals
• A Cluster Bootstrap for Two-Loop MHV Amplitudes
• Taming Calabi-Yau Feynman integrals: The four-loop equal-mass banana integral
• Yangian-invariant fishnet integrals in 2 dimensions as volumes of Calabi-Yau varieties
• Multi-Loop Positivity of the Planar $\mathcal{N}=4$ SYM Six-Point Amplitude
• Bootstrapping a Stress-Tensor Form Factor through Eight Loops
• An analytic result for the two-loop seven-point MHV amplitude in N=4 SYM
• Loop-by-loop Differential Equations for Dual (Elliptic) Feynman Integrals
• Singularities of eight- and nine-particle amplitudes from cluster algebras and tropical geometry
• Antipodal Self-Duality for a Four-Particle Form Factor
• The Sklyanin Bracket and Cluster Adjacency at All Multiplicity
• Traintrack Calabi-Yaus from Twistor Geometry
• Symbology for elliptic multiple polylogarithms and the symbol prime
• Modular transformations of elliptic Feynman integrals
• Schubert Problems, Positivity and Symbol Letters
• Bootstrapping a Two-Loop Four-Point Form Factor
• The SAGEX Review on Scattering Amplitudes, Chapter 5: Analytic Bootstraps for Scattering Amplitudes and Beyond
• A nice two-loop next-to-next-to-MHV amplitude in $\mathcal{N}=4$ super-Yang-Mills

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• Calabi-Yau Feynman integrals in gravity: $\epsilon$-factorized form for apparent singularities
• SOFIA: Singularities of Feynman Integrals Automatized
• Canonical differential equations for the elliptic two-loop five-point integral family relevant to $t\bar{t}+$jet production at leading colour
• Classification of Feynman integral geometries for black-hole scattering at 5PM order
• Electroweak double-box integrals for Moller scattering
• An Elliptic One-Loop Amplitude in Anti-de-Sitter Space
• The spectrum of Feynman-integral geometries at two loops