A Mini-Introduction To Superfield Decompositions With Branching Rules

TL;DR

This paper introduces a systematic method for decomposing superfield components using Lie algebra branching rules, aiding the search for supergravity supermultiplets, and provides a Mathematica implementation for practical use.

Contribution

It presents a novel systematic approach for superfield decomposition based on Lie algebra branching rules and offers a practical Mathematica implementation.

Findings

Method enables expansion of superfields into subalgebra components.

Facilitates search for off-shell supergravity supermultiplets.

Provides a usable Mathematica code for superfield decomposition.

Abstract

This paper provides a short introduction to scalar, bosonic, and fermionic superfield component expansion based on the branching rules of irreducible representations in one Lie algebra (in our case, $\mathfrak{su}(32)$, and also $\mathfrak{su}(16)$) into one of its Lie subalgebras ($\mathfrak{so}(11)$, $\mathfrak{so}(10)$). This systematic method paves the way for expansion of bosonic and fermionic superfields, in order to search for possible off-shell supergravity supermultiplets. Furthermore, we implement such a decomposition method in Mathematica in its simplest form, which can be used for superfield component decompositions.