Supergravity Component Reduction with Computer Algebra

TL;DR

This paper demonstrates how to utilize computer algebra, specifically Cadabra, to systematically perform component reduction in 5D, N=1 supergravity, facilitating the construction of supersymmetric invariants.

Contribution

It introduces a method for using computer algebra to streamline component reduction in supergravity, enhancing the process of constructing supersymmetric invariants.

Findings

Successful implementation of Cadabra for supergravity component reduction

Systematic approach to superspace to component transition in 5D supergravity

Facilitates construction of curvature-squared invariants

Abstract

Using an interplay between superspace and component superconformal tensor calculus techniques, recently, the off-shell construction of the supersymmetric extension of the three independent curvature-squared invariants for minimal (N = 1) gauged supergravity in five dimensions (5D) was completed. A key ingredient in obtaining these results is the implementation of computer algebra algorithms. In this report, we describe how to use cadabra to systematically study component reduction from superspace with computer algebra in the case of 5D, N = 1 supergravity.