WiLE: a Mathematica package for weak coupling expansion of Wilson loops in ABJ(M) theory

TL;DR

WiLE is a Mathematica package that automates the weak coupling expansion of Wilson loops in ABJ(M) theory, facilitating diagram generation and integral computation at arbitrary orders.

Contribution

It introduces a user-friendly Mathematica tool for systematic weak coupling expansion of Wilson loops in ABJ(M) theory, including diagram classification and integral representation.

Findings

Automates diagram generation and integral representation for Wilson loops

Supports calculation of ladder diagrams at three-loop order

Validates recent theoretical results in ABJ(M) Wilson loop studies

Abstract

We present WiLE, a Mathematica package designed to perform the weak coupling expansion of any Wilson loop in ABJ(M) theory at arbitrary perturbative order. For a given set of fields on the loop and internal vertices, the package displays all the possible Feynman diagrams and their integral representations. The user can also choose to exclude non planar diagrams, tadpoles and self-energies. Through the use of interactive input windows, the package should be easily accessible to users with little or no previous experience. The package manual provides some pedagogical examples and the computation of all ladder diagrams at three-loop relevant for the cusp anomalous dimension in ABJ(M). The latter application gives also support to some recent results computed in different contexts.