In a novel scaling limit on the Coulomb branch of planar N=4 SYM, the Sudakov form factor and four-point amplitude exhibit double-logarithmic behavior governed by a walking anomalous dimension that interpolates between cusp and octagon anomalous dimensions, with proposed all-loop expressions relying
Salvatori,The Tropical Geometry of Subtraction Schemes,2406.14606
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Tropicalized massive scalar QFT is exactly solvable via a non-linear recursion for effective action coefficients that computes graph moduli space volumes, enabling a polynomial-time sampling algorithm for high-order perturbative contributions.
Chebyshev polynomial approximations with adaptive sampling solve canonical differential equations for Feynman integrals, demonstrated to be stable and competitive for two-loop five-point cases in double precision.
Three-loop five-point dual conformal master integrals on the Coulomb branch of N=4 SYM are computed via DCI-preserving regularization, cross-ratio factorization, and HyperInt for residual regions.
Characterizes numerators yielding finite or evanescent massless pentabox integrals, gives compact generators via momentum basis and Gram determinants, and evaluates lowest-rank cases in polylogarithms and pentagon functions.
SubTropica is a software package that automates symbolic integration of linearly-reducible Euler integrals via tropical subtraction, supported by HyperIntica and an AI-driven Feynman integral database.
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Walking Sudakov: From Cusp to Octagon
In a novel scaling limit on the Coulomb branch of planar N=4 SYM, the Sudakov form factor and four-point amplitude exhibit double-logarithmic behavior governed by a walking anomalous dimension that interpolates between cusp and octagon anomalous dimensions, with proposed all-loop expressions relying
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Tropicalized quantum field theory and global tropical sampling
Tropicalized massive scalar QFT is exactly solvable via a non-linear recursion for effective action coefficients that computes graph moduli space volumes, enabling a polynomial-time sampling algorithm for high-order perturbative contributions.
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Chebyshev Approximations of Feynman Integrals for Collider Physics
Chebyshev polynomial approximations with adaptive sampling solve canonical differential equations for Feynman integrals, demonstrated to be stable and competitive for two-loop five-point cases in double precision.
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Five legs @ three loops: slightly off-shell dual conformal integrals
Three-loop five-point dual conformal master integrals on the Coulomb branch of N=4 SYM are computed via DCI-preserving regularization, cross-ratio factorization, and HyperInt for residual regions.
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Finite Massless Pentaboxes
Characterizes numerators yielding finite or evanescent massless pentabox integrals, gives compact generators via momentum basis and Gram determinants, and evaluates lowest-rank cases in polylogarithms and pentagon functions.
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SubTropica
SubTropica is a software package that automates symbolic integration of linearly-reducible Euler integrals via tropical subtraction, supported by HyperIntica and an AI-driven Feynman integral database.