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We investigate from a mathematical perspective how Feynman amplitudes appear in the low-energy limit of string amplitudes. In this paper, we prove the convergence of the integrands. We derive this from results describing the asymptotic behavior of the height pairing between degree-zero divisors, as a family of Riemann surfaces degenerates. These are obtained by means of the nilpotent orbit theorem in Hodge theory.
Recently Bonisch-Fischbach-Klemm-Nega-Safari discovered, via numerical computation, that the leading asymptotics of the l-loop Banana Feynman amplitude at the large complex structure limit can be described by the Gamma class of a degree (1,...,1) Fan
We study solutions to the Kadomtsev-Petviashvili equation whose underlying algebraic curves undergo tropical degenerations. Riemanns theta function becomes a finite exponential sum that is supported on a Delaunay polytope. We introduce the Hirota var
We study Feynman integrals and scattering amplitudes in ${cal N}=4$ super-Yang-Mills by exploiting the duality with null polygonal Wilson loops. Certain Feynman integrals, including one-loop and two-loop chiral pentagons, are given by Feynman diagram
We study shift relations between Feynman integrals via the Mellin transform through parametric annihilation operators. These contain the momentum space IBP relations, which are well-known in the physics literature. Applying a result of Loeser and Sab
We construct a three parameter deformation of the Hopf algebra $mathbf{LDIAG}$. This new algebra is a true Hopf deformation which reduces to $mathbf{LDIAG}$ on one hand and to $mathbf{MQSym}$ on the other, relating $mathbf{LDIAG}$ to other Hopf algeb