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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A parity-split IBP system for n-propagator families in de Sitter space is identified, along with a conjecture that dlog-form differential equations extend to dS integrands with Hankel functions, verified for the one-loop bubble.
Discrete symmetries of Feynman integral families correspond to permutations of Feynman parameters and induce group actions on twisted cohomology whose characters are Euler characteristics of fixed-point sets, yielding a formula for master integral counts in symmetric banana diagrams up to four loops
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.
Feynman integrals with mixed geometries (K3 surfaces, curves, points) can be computed more efficiently by extracting and using their algebraic geometric properties.
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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Loop integrals in de Sitter spacetime: The parity-split IBP system and $\mathrm{d}\log$-form differential equations
A parity-split IBP system for n-propagator families in de Sitter space is identified, along with a conjecture that dlog-form differential equations extend to dS integrands with Hankel functions, verified for the one-loop bubble.
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Discrete symmetries of Feynman integrals
Discrete symmetries of Feynman integral families correspond to permutations of Feynman parameters and induce group actions on twisted cohomology whose characters are Euler characteristics of fixed-point sets, yielding a formula for master integral counts in symmetric banana diagrams up to four loops
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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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From geometry to phenomenology
Feynman integrals with mixed geometries (K3 surfaces, curves, points) can be computed more efficiently by extracting and using their algebraic geometric properties.