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

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. Program summaryProgram Title: WiLEProgram Files doi:http://dx.doi.org/10.17632/xm53d23hph.1Licensing provisions: GNU LGPLProgramming language: Wolfram Mathematica version 8.0 or higherNature of problem: In ABJ(M) theory one can define bosonic and fermionic Wilson loops. In order to study those operators using the standard perturbation theory techniques, one has to expand the Wilson loops at weak coupling and perform all the Wick contractions. Since the theory possesses a quiver structure and its Lagrangian contains many different vertices, this procedure could be very involved. Then we propose a Mathematica package to automatize this computation.Solution method: The aim of the package WiLE is to obtain the weak coupling expansion of the Wilson loops in terms of Feynman diagrams. Given a set of initial data, as the set of vertices involved in the diagram and the fields contributing in the Wilson loop expansion, the package computes the related diagrams and their integral representations.Additional comments: Web page: https://github.com/miciosca/WiLE, contact: michelangelo.preti@desy.de — for bugs, possible improvements and questions.