Related papers: Symbology for elliptic multiple polylogarithms and…
We present full analytic results for the four-point one-loop amplitude of a conformally coupled scalar in four-dimensional Anti-de-Sitter space dual to a primary operator with scaling dimension 1. The computation is based on an intriguing…
We summarize recent computations with a class of elliptic generalizations of polylogarithms, arising from the massive sunrise integral. For the case of arbitrary masses we obtain results in two and four space-time dimensions. The iterated…
The full 245-letter symbol alphabet for all planar massless two-loop six-point Feynman integrals was recently determined in arXiv:2412.19884 and arXiv:2501.01847. In a parallel mathematical development, it was shown in arXiv:2408.14956 that…
We introduce a machine-learning framework based on symbolic regression to extract the full symbol alphabet of multi-loop Feynman integrals. By targeting the analytic structure rather than reduction, the method is broadly applicable and…
We study Feynman integrals in the representation with Schwinger parameters and derive recursive integral formulas for massless 3- and 4-point functions. Properties of analytic (including dimensional) regularization are summarized and we…
The three-loop four-point function of stress-tensor multiplets in N=4 super Yang-Mills theory contains two so far unknown, off-shell, conformal integrals, in addition to the known, ladder-type integrals. In this paper we evaluate the…
We investigate the behaviour of elliptic Feynman integrals under modular transformations. This has a practical motivation: Through a suitable modular transformation we can achieve that the nome squared is a small quantity, leading to fast…
The $\varepsilon$-form of a system of differential equations for Feynman integrals has led to tremendeous progress in our abilities to compute Feynman integrals, as long as they fall into the class of multiple polylogarithms. It is…
In modern quantum field theory, one of the most important tasks is the calculation of loop integrals. Loop integrals appear when evaluating the Feynman diagrams with one or more loops by integrating over the internal momenta. Even though…
The high-energy behaviour of scattering amplitudes involving massive particles has attracted interest in recent years. In these proceedings, we report on the analytic tool AsyInt for solving massive multi-loop Feynman integrals in the…
We provide evidence through two loops, that rational letters of polylogarithmic Feynman integrals are captured by the Landau equations, when the latter are recast as a polynomial of the kinematic variables of the integral, known as the…
We introduce a method for deriving constraints on the symbol of Feynman integrals from the form of their asymptotic expansions in the neighborhood of Landau loci. In particular, we show that the behavior of these integrals near singular…
The main steps of the process of obtaining the result [1] in terms of elliptic polylogarithms for a two-loop sunrise integral with two different internal masses with pseudothreshold kinematics for all orders of the dimensional regulator are…
Multiple elliptic polylogarithms can be written as (multiple) integrals of products of basic hypergeometric functions. The latter are computable, to arbitrary precision, using a q-difference equation and q-contiguous relations.
We comment on the status of "Steinmann-like" constraints, i.e. all-loop constraints on consecutive entries of the symbol of scattering amplitudes and Feynman integrals in planar ${\cal N}=4$ super-Yang-Mills, which have been crucial for the…
We present a new algorithm for integration-by-parts (IBP) reduction of Feynman integrals with high powers of numerators or propagators, a demanding computational step in evaluating multi-loop scattering amplitudes. The algorithm starts with…
In these lectures I discuss Feynman graphs and the associated Feynman integrals. Of particular interest are the classes functions, which appear in the evaluation of Feynman integrals. The most prominent class of functions is given by…
We present SubTropica, a Mathematica package that performs symbolic integration of multi-polylogarithmic integrals using recent advances in tropical geometry. It focuses on the class of linearly-reducible Euler integrals, such as Feynman…
It is shown that, under some mild technical conditions, representations of prime numbers by binary quadratic forms can be computed in polynomial complexity by exploiting Schoof's algorithm, which counts the number of $\mathbb F_q$-points of…
We calculate the general planar dual-conformally invariant double-pentagon and pentabox integrals in four dimensions. Concretely, we derive one-fold integral representations for these elliptic integrals over polylogarithms of weight three.…