arXiv subjects

Konstantin Baune

Publications and source records attributed to Konstantin Baune.

8 recordsLinked to original sources

arXiv2026

Single-valued polylogarithms for higher genera

We extend the construction of single-valued polylogarithms at genus one from arXiv:2511.15240 to once-punctured Riemann surfaces of higher genera. The resulting functions have a trivial monodromy representation with respect to the fundamental group, hence they descend to well-defined functions on the surface. Our construction of single-valued polylogarithms is based on Enriquez' connection and relates them to the polylogarithms from D'Hoker-Hidding-Schlotterer. Finally, we identify the Arakelov Green's function within our framework.

hep-th↗

arXiv2025

A construction of single-valued elliptic polylogarithms

We establish a general construction of single-valued elliptic polylogarithms as functions on the once-punctured elliptic curve. Our formalism is an extension of Brown's construction of genus-zero single-valued polylogarithms to the elliptic curve: the condition of trivial monodromy for solutions to the Knizhnik-Zamolodchikov-Bernard equation is expressed in terms of elliptic associators and involves two representations of a two-letter alphabet. Our elliptic single-valued condition reduces to Brown's genus-zero condition upon degeneration of the torus. We provide several examples for our construction, including the elliptic Bloch-Wigner dilogarithm.

hep-th↗

arXiv2025

Higher-genus multiple zeta values

Multiple zeta values arise as special values of polylogarithms defined on Riemann surfaces of various genera. Building on the vast knowledge for classical and elliptic multiple zeta values, we explore a canonical extension of the formalism to Riemann surfaces of higher genera, which yields higher-genus multiple zeta values. We provide a regularization prescription for higher-genus polylogarithms, which we extend to higher-genus multiple zeta values. Our regularization uses the Schottky uniformization to trace back higher-genus endpoint regularization to known regularization at genus one. Additionally, we are commenting on relations among higher-genus multiple zeta values implied by degeneration of the underlying geometry, where we distinguish between the two types of separating and non-separating degeneration. Finally, employing functional relations for higher-genus polylogarithms in the Schottky uniformization, we explore relations among higher-genus multiple zeta values and check them against our numerical testing setup. We identify relations for higher-genus multiple zeta values beyond those implied by polylogarithm identities, thereby matching the situation for genus zero and genus one. While we find several known structures for elliptic multiple zeta values to generalize to relations for higher-genus multiple zeta values, there are further classes of relations arising from the interplay and combinatorics of different cycles.

hep-th↗

arXiv2025

Associators for AdS string amplitude building blocks

We show that building blocks for open- and closed-string amplitudes on AdS are generated by the Drinfeld and Deligne associator, respectively. Our formalism lifts the known associator recursions for flat-space string amplitudes to the AdS picture. This delivers another proof that the AdS building blocks admit low-energy expansions with (single-valued) multiple zeta values as coefficients and provides all-order relations for the integral expressions.

hep-th↗

arXiv2024

Closed-string amplitude recursions from the Deligne associator

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 closed-string tree-level amplitudes. We achieve this by showing that closed-string analogues of Selberg integrals satisfy the Knizhnik-Zamolodchikov equation for a suitable matrix representation of the free Lie algebra on two generators, and by identifying the limits at z=1 and z=0, which are related by the Deligne associator, with N-point and (N-1)-point closed-string amplitudes, respectively.

hep-th↗

arXiv2024

Higher-genus Fay-like identities from meromorphic generating functions

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 polylogarithms rely on identities for those integration kernels. In this article, we derive identities for Enriquez' meromorphic generating function and investigate the implications for the associated integration kernels. The resulting identities are shown to be exhaustive and therefore reproduce all identities for Enriquez' kernels conjectured in arXiv:2407.11476 recently.

hep-th↗

arXiv2024

Schottky-Kronecker forms and hyperelliptic polylogarithms

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 Schottky parametrization of a Riemann surface to construct higher-genus analogues of Kronecker's generating series, which we refer to as Schottky-Kronecker forms. Our explicit construction generalizes ideas from Bernard's higher-genus construction of the Knizhnik-Zamolodchikov connection. Integration kernels generated from the Schottky-Kronecker forms are defined as Poincaré series. Under technical assumptions, related to the convergence of these Poincaré series on the underlying Riemann surface, we argue that these integration kernels coincide with a set of differentials defined by Enriquez, whose iterated integrals constitute higher-genus analogues of polylogarithms. Enriquez' original definition is not well-suited for numerical evaluation of higher-genus polylogarithms. In contrast, the Poincaré series defining our integration kernels can be evaluated numerically for real hyperelliptic curves, for which the above-mentioned convergence assumptions can be verified. We numerically evaluate several examples of genus-two polylogarithms, thereby paving the way for numerical evaluation of hyperelliptic analogues of polylogarithms.

hep-th↗

arXiv2023

A KLT-like construction for multi-Regge amplitudes

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 scattering amplitudes with multi-valued coefficients. We consider the simplest non-trivial situation: the six-point remainder function complementing the Bern-Dixon-Smirnov ansatz for multi-loop amplitudes. Utilizing inverse Mellin transformations, all single-valued amplitude components can indeed be decomposed into multi-valued amplitude components. Although the final expression is very similar in structure to the Kawai-Lewellen-Tye construction, moving away from the highly symmetric string scenario comes with several imponderabilities, some of which become more pronounced when considering more than six external legs in the remainder function.

hep-th↗