Two-loop Feynman integrals involve Riemann spheres, elliptic curves, hyperelliptic curves of genus 2 and 3, K3 surfaces, and a rationalizable Del Pezzo surface of degree 2.
Canonical differential equations beyond genus one
6 Pith papers cite this work. Polarity classification is still indexing.
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Feynman integrals selected for unit leading singularities in complex geometries satisfy epsilon-factorized differential equations with new transcendental functions corresponding to periods and differential forms in the Gauss-Manin connection.
A construction of single-valued elliptic polylogarithms on the punctured elliptic curve is given that reduces to Brown's genus-zero condition upon torus degeneration.
A geometric order relation in IBP reduction yields a master-integral basis with Laurent-polynomial differential equations on the maximal cut that are then ε-factorized.
Proposes motivic coaction formulae for genus-one iterated integrals over holomorphic Eisenstein series using zeta generators, verifies expected coaction properties, and deduces f-alphabet decompositions of multiple modular values.
The extra-involution mechanism for genus drop is a special case of unramified double covering between curves, which explains genus drops with non-hyperelliptic to hyperelliptic transitions in certain three-loop Feynman integrals.
citing papers explorer
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The spectrum of Feynman-integral geometries at two loops
Two-loop Feynman integrals involve Riemann spheres, elliptic curves, hyperelliptic curves of genus 2 and 3, K3 surfaces, and a rationalizable Del Pezzo surface of degree 2.
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Integrand Analysis, Leading Singularities and Canonical Bases beyond Polylogarithms
Feynman integrals selected for unit leading singularities in complex geometries satisfy epsilon-factorized differential equations with new transcendental functions corresponding to periods and differential forms in the Gauss-Manin connection.
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A construction of single-valued elliptic polylogarithms
A construction of single-valued elliptic polylogarithms on the punctured elliptic curve is given that reduces to Brown's genus-zero condition upon torus degeneration.
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New algorithms for Feynman integral reduction and $\varepsilon$-factorised differential equations
A geometric order relation in IBP reduction yields a master-integral basis with Laurent-polynomial differential equations on the maximal cut that are then ε-factorized.
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Towards Motivic Coactions at Genus One from Zeta Generators
Proposes motivic coaction formulae for genus-one iterated integrals over holomorphic Eisenstein series using zeta generators, verifies expected coaction properties, and deduces f-alphabet decompositions of multiple modular values.
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Genus drop involving non-hyperelliptic curves in Feynman integrals
The extra-involution mechanism for genus drop is a special case of unramified double covering between curves, which explains genus drops with non-hyperelliptic to hyperelliptic transitions in certain three-loop Feynman integrals.