FieldsX -- An extension package for the xAct tensor computer algebra suite to include fermions, gauge fields and BRST cohomology

Abstract

I present the tensor computer algebra package FieldsX, which extends the xAct suite of tensor algebra packages to perform computations in field theory with fermions and gauge fields. This includes the standard tools of curved-space $\gamma$ matrices, Fierz identities, invariant tensors on Lie algebras, arbitrary gradings and left and right variational derivatives, as well as the decomposition of spinor products into irreducible components following the approach of d'Auria, Fré, Maina and Regge [Annals Phys. 139 (1982) 93]. Lastly, it also includes functions to work with nilpotent differentials such as the BV-BRST differential for (supersymmetric) gauge theories and to compute their (relative) cohomologies, from which anomalies and gauge-invariant operators can be determined. I illustrate the use of the package with the example of $\mathcal{N}=1$ Super-Yang--Mills theory.

arXiv comment17 pages of example computations, 36 pages of reference for each included function. v2: Compatibility with xAct Spinors package, v3: Functions to work with frame fields and spin connections, updated example, now includes example notebook

References in corpus (12)

• Local BRST cohomology in gauge theories
• Consistent couplings between fields with a gauge freedom and deformations of the master equation
• xTras: a field-theory inspired xAct package for Mathematica
• xPerm: fast index canonicalization for tensor computer algebra
• A field-theory motivated approach to symbolic computer algebra
• xPert: Computer algebra for metric perturbation theory
• The Invar Tensor Package
• The Invar tensor package: Differential invariants of Riemann
• Global Symmetries in the Antifield-Formalism
• Extended antifield-formalism
• BRST Symmetry and Cohomology
• Spinors: a Mathematica package for doing spinor calculus in General Relativity

Cited by in corpus (6)

• Ghost and Tachyon Free Propagation up to spin-3 in Lorentz Invariant Field Theories
• Heat kernel coefficients for massive gravity
• Analysis of Unitarity in Conformal Quantum Gravity
• Unitarity through PT symmetry in Quantum Quadratic Gravity
• Deformations of Supergravity and Supersymmetry Anomalies
• Anomalies and Supersymmetry