A Mathematica Package for Computing N=2 Superfield Operator Product Expansions

TL;DR

This paper introduces a Mathematica package that automates the computation of superfield operator product expansions in N=2 superconformal field theory, facilitating complex algebraic manipulations and verifications.

Contribution

The paper presents a new Mathematica tool that automates SOPE calculations, checks Jacobi identities, and handles complex superfield composites in N=2 superconformal theories.

Findings

Successfully constructed the small N=4 superconformal algebra from N=2 superfields.

Realized the N=2 superconformal algebra using chiral and antichiral fermionic superfields.

Automated SOPE computations and standardization of normal ordered products.

Abstract

We describe a general purpose Mathematica package for computing Superfield Operator Product Expansions in meromorphic $N=2$ superconformal field theory. Given the SOPEs for a set of ``basic" superfields, SOPEs of arbitrarily complicated composites can be computed automatically. Normal ordered products are always reduced to a standard form. It is possible to check the Jacobi identities, and to compute Poisson brackets (``classical SOPEs''). We present two explicit examples: a construction of the ``small'' $N=4$ superconformal algebra in terms of $N=2$ superfields, and a realisation of the $N=2$ superconformal algebra in terms of chiral and antichiral fermionic superfields.