Lambda: A Mathematica package for operator product expansions in vertex algebras

Abstract

We give an introduction to the Mathematica package Lambda, designed for calculating λ-brackets in both vertex algebras, and in SUSY vertex algebras. This is equivalent to calculating operator product expansions in two-dimensional conformal field theory. The syntax of λ-brackets is reviewed, and some simple examples are shown, both in component notation, and in N = 1 superfield notation. Program summary Program title: Lambda Catalogue identifier: AEHF_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEHF_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License No. of lines in distributed program, including test data, etc.: 18 087 No. of bytes in distributed program, including test data, etc.: 131 812 Distribution format: tar.gz Programming language: Mathematica Computer: See specifications for running Mathematica V7 or above. Operating system: See specifications for running Mathematica V7 or above. RAM: Varies greatly depending on calculation to be performed. Classification: 4.2, 5, 11.1. Nature of problem: Calculate operator product expansions (OPEs) of composite fields in 2d conformal field theory. Solution method: Implementation of the algebraic formulation of OPEs given by vertex algebras, and especially by λ-brackets. Running time: Varies greatly depending on calculation requested. The example notebook provided takes about 3 s to run.