Johannes Broedel
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View article: Higher-genus Fay-like identities from meromorphic generating functions
Higher-genus Fay-like identities from meromorphic generating functions Open
A possible way of constructing polylogarithms on Riemann surfaces of higher genera facilitates integration kernels, which can be derived from generating functions incorporating the geometry of the surface. Functional relations among polylo…
View article: Closed-string amplitude recursions from the Deligne associator
Closed-string amplitude recursions from the Deligne associator Open
Inspired by earlier results on recursions for open-string tree-level amplitudes, and by a result of Brown and Dupont relating open- and closed-string tree-level amplitudes via single-valued periods, we identify a recursive relation for clo…
View article: Schottky–Kronecker forms and hyperelliptic polylogarithms
Schottky–Kronecker forms and hyperelliptic polylogarithms Open
Elliptic polylogarithms can be defined as iterated integrals on a genus-one Riemann surface of a set of integration kernels whose generating series was already considered by Kronecker in the 19th century. In this article, we employ the Sch…
View article: Higher-genus Fay-like identities from meromorphic generating functions
Higher-genus Fay-like identities from meromorphic generating functions Open
A possible way of constructing polylogarithms on Riemann surfaces of higher genera facilitates integration kernels, which can be derived from generating functions incorporating the geometry of the surface. Functional relations between poly…
View article: Schottky-Kronecker forms and hyperelliptic polylogarithms
Schottky-Kronecker forms and hyperelliptic polylogarithms Open
Elliptic polylogarithms can be defined as iterated integrals on a genus-one Riemann surface of a set of integration kernels whose generating series was already considered by Kronecker in the 19th century. In this article, we employ the Sch…
View article: A KLT-like construction for multi-Regge amplitudes
A KLT-like construction for multi-Regge amplitudes Open
Inspired by the calculational steps originally performed by Kawai, Lewellen and Tye, we decompose scattering amplitudes with single-valued coefficients obtained in the multi-Regge-limit of N=4 super-Yang-Mills theory into products of scatt…
View article: A KLT-like construction for multi-Regge amplitudes
A KLT-like construction for multi-Regge amplitudes Open
Inspired by the calculational steps originally performed by Kawai, Lewellen and Tye, we decompose scattering amplitudes with single-valued coefficients obtained in the multi-Regge-limit of N=4 super-Yang–Mills theory into products of scatt…
View article: Elliptic polylogarithms and Feynman parameter integrals
Elliptic polylogarithms and Feynman parameter integrals Open
In this paper we study the calculation of multiloop Feynman integrals that cannot be expressed in terms of multiple polylogarithms. We show in detail how certain types of two- and three-point functions at two loops, which appear in the cal…
View article: Elliptic polylogarithms and iterated integrals on elliptic curves. Part I: general formalism
Elliptic polylogarithms and iterated integrals on elliptic curves. Part I: general formalism Open
We introduce a class of iterated integrals, defined through a set of linearly independent integration kernels on elliptic curves. As a direct generalization of multiple polylogarithms, we construct our set of integration kernels ensuring t…
View article: Elliptic symbol calculus: from elliptic polylogarithms to iterated integrals of Eisenstein series
Elliptic symbol calculus: from elliptic polylogarithms to iterated integrals of Eisenstein series Open
We present a generalization of the symbol calculus from ordinary multiple polylogarithms to their elliptic counterparts. Here, our formalism is based on a special case of a coaction on large classes of periods that is applied in particular…
View article: Functions Beyond Multiple Polylogarithms for Precision Collider Physics
Functions Beyond Multiple Polylogarithms for Precision Collider Physics Open
Feynman diagrams constitute one of the essential ingredients for making precision predictions for collider experiments. Yet, while the simplest Feynman diagrams can be evaluated in terms of multiple polylogarithms -- whose properties as sp…
View article: Meromorphic modular forms and the three-loop equal-mass banana integral
Meromorphic modular forms and the three-loop equal-mass banana integral Open
We consider a class of differential equations for multi-loop Feynman integrals which can be solved to all orders in dimensional regularisation in terms of iterated integrals of meromorphic modular forms. We show that the subgroup under whi…
View article: Meromorphic modular forms and the three-loop equal-mass banana integral
Meromorphic modular forms and the three-loop equal-mass banana integral Open
A bstract We consider a class of differential equations for multi-loop Feynman integrals which can be solved to all orders in dimensional regularisation in terms of iterated integrals of meromorphic modular forms. We show that the subgroup…
View article: Amplitude recursions with an extra marked point
Amplitude recursions with an extra marked point Open
The recursive calculation of Selberg integrals by Aomoto and Terasoma using the Knizhnik-Zamolodchikov equation and the Drinfeld associator makes use of an auxiliary point and facilitates the recursive evaluation of string amplitudes at ge…
View article: A geometrical framework for amplitude recursions: bridging between trees and loops
A geometrical framework for amplitude recursions: bridging between trees and loops Open
Various methods for the recursive evaluation of scattering amplitudes in quantum field theory and string theory have been put forward during the last couple of years. In these proceedings we describe a geometrical framework, which is belie…
View article: Functional relations for elliptic polylogarithms
Functional relations for elliptic polylogarithms Open
Numerous examples of functional relations for multiple polylogarithms are known. For elliptic polylogarithms, however, tools for the exploration of functional relations are available, but only very few relations are identified. Starting fr…
View article: Elliptic Feynman integrals and pure functions
Elliptic Feynman integrals and pure functions Open
A bstract We propose a variant of elliptic multiple polylogarithms that have at most logarithmic singularities in all variables and satisfy a differential equation without homogeneous term. We investigate several non-trivial elliptic two-l…
View article: Elliptic polylogarithms and two-loop Feynman integrals
Elliptic polylogarithms and two-loop Feynman integrals Open
We review certain classes of iterated integrals that appear in the computation of Feynman integrals that involve elliptic functions. These functions generalise the well-known class of multiple polylogarithms to elliptic curves and are clos…
View article: Cuts and Feynman amplitudes beyond polylogarithms
Cuts and Feynman amplitudes beyond polylogarithms Open
In this contribution to the proceedings of Loops and Legs in Quantum Field Theory 2018, we discuss some recent developments in the calculation of multiloop Feynman integrals which evaluate to functions beyond multiple polylogarithms.
View article: Elliptic polylogarithms and two-loop Feynman integrals
Elliptic polylogarithms and two-loop Feynman integrals Open
We review certain classes of iterated integrals that appear in the computation of Feynman integrals that involve elliptic functions. These functions generalise the well-known class of multiple polylogarithms to elliptic curves and are clos…
View article: From modular forms to differential equations for Feynman integrals
From modular forms to differential equations for Feynman integrals Open
In these proceedings we discuss a representation for modular forms that is more suitable for their application to the calculation of Feynman integrals in the context of iterated integrals and the differential equation method. In particular…
View article: Elliptic polylogarithms and iterated integrals on elliptic curves. II. An application to the sunrise integral
Elliptic polylogarithms and iterated integrals on elliptic curves. II. An application to the sunrise integral Open
We introduce a class of iterated integrals that generalize multiple polylogarithms to elliptic curves. These elliptic multiple polylogarithms are closely related to similar functions defined in pure mathematics and string theory. We then f…
View article: From elliptic iterated integrals to elliptic multiple zeta values
From elliptic iterated integrals to elliptic multiple zeta values Open
While transcendental numbers are omnipresent in modern field-theory amplitude calculations, it is scattering amplitudes in string theory, which provide the most straightfoward setting for bridging the gap between conventional quantum field…
View article: Six-point remainder function in multi-Regge-kinematics: an efficient approach in momentum space
Six-point remainder function in multi-Regge-kinematics: an efficient approach in momentum space Open
Starting from the known all-order expressions for the BFKL eigenvalue and impact factor, we establish a formalism allowing the direct calculation of the six-point remainder function in $$ \mathcal{N} $$ = 4 super-Yang-Mills theory in momen…
View article: Relations between elliptic multiple zeta values and a special derivation algebra
Relations between elliptic multiple zeta values and a special derivation algebra Open
We investigate relations between elliptic multiple zeta values and describe a method to derive the number of indecomposable elements of given weight and length. Our method is based on representing elliptic multiple zeta values as iterated …