Elliptic polylogarithms and iterated integrals on elliptic curves. II. An application to the sunrise integral

By Johannes Broedel, Claude Duhr, Falko Dulat, L. Tancredi. Physical Review D, 2017

136 citations recorded by the source corpus.

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 math- ematics and string theory. We then focus on the equal-mass and non-equal-mass sunrise integrals, and we develop a formalism that enables us to compute these Feynman integrals in terms of our iterated integrals on elliptic curves. The key idea is to use integration-by-parts identities to identify a set of integral kernels, whose precise form is determined by the branch points of the integral in question. These kernels allow us to express all iterated integrals on an elliptic curve in terms of them. The flexibility of our approach leads us to expect that it will be applicable to a large variety of integrals in high-energy physics.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/bf6e0d1dba7cb0c416ea0a4f46f71f8283061864

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Falko Dulat
2. Claude Duhr
3. Johannes Broedel
4. L. Tancredi
5. B. Penante
6. Gudrun Heinrich

In Geometry and Topology

1. Falko Dulat
2. Johannes Broedel
3. L. Tancredi
4. B. Penante
5. Claude Duhr
6. L. Dixon
7. Gudrun Heinrich
8. S. Stieberger

Citations in the corpus

• Elliptic polylogarithms and iterated integrals on elliptic curves. Part I: general formalism (2017, methodology): “ples In this section we discuss some examples of how to work with elliptic polylogarithms. The examples are of mostly mathematical nature. For an application to the sunrise integral, we refer to ref. [40]. 8.1 MPLs depending on square roots of cubic or quartic polynomials We have already seen that o”
• Elliptic symbol calculus: from elliptic polylogarithms to iterated integrals of Eisenstein series (2018, background): “[47] in order to avoid confusion later in the text.”