Computer algebra calculations in supersymmetric electrodynamics

TL;DR

This paper introduces a new symbolic algorithm and C++ program to automate the generation and calculation of supersymmetric Feynman diagrams in ${\cal N}=1$ supersymmetric electrodynamics, facilitating higher-loop computations.

Contribution

The authors developed a novel algorithm and software for symbolic calculations of supersymmetric Feynman diagrams, specifically for ${\cal N}=1$ supersymmetric electrodynamics with higher-derivative regularization.

Findings

Successfully calculated the three-loop anomalous dimension in ${\cal N}=1$ supersymmetric QED.

Automated diagram generation and reduction to Euclidean momentum integrals.

Demonstrated the program's effectiveness in complex higher-loop calculations.

Abstract

We propose a new symbolic algorithm and a C++ program for generating and calculating supersymmetric Feynman diagrams for ${\cal N}=1$ supersymmetric electrodynamics regularized by higher derivatives in four dimensions. According to standard rules, the program generates all diagrams that are necessary to calculate a specific contribution to the two-point Green function of matter superfields in the needed order, and then reduces the answer to the sum of Euclidean momentum integrals. At the moment, the program was used to calculate the anomalous dimension in ${\cal N}=1$ supersymmetric quantum electrodynamics, regularized by higher derivatives, in the three-loop approximation.