Superfield Component Decompositions and the Scan for Prepotential Supermultiplets in 10D Superspaces

TL;DR

This paper provides a comprehensive SO(1,9) Lorentz description of superfield components in 10D superspaces, introduces Adinkra graphs for these spaces, and develops a method to identify superfields containing gravitons and gravitinos for supergravity and Yang-Mills theories.

Contribution

It presents the first explicit Lorentz descriptions of superfield components in 10D superspaces and introduces Adinkra graphs for these spaces, enabling new scans for supergravity prepotentials.

Findings

Explicit SO(1,9) descriptions of superfield components in 10D

First definition of Adinkra graphs for ten-dimensional superspaces

Method to identify superfields containing gravitons and gravitinos

Abstract

The first complete and explicit SO(1,9) Lorentz descriptions of all component fields contained in $\mathcal{N} = 1$, $\mathcal{N} = 2$A, and $\mathcal{N} = 2$B unconstrained scalar 10D superfields are presented. These are made possible by the discovery of the relation of the superfield component expansion as a consequence of the branching rules of irreducible representations in one ordinary Lie algebra into one of its Lie subalgebras. Adinkra graphs for ten dimensional superspaces are defined for the first time, whose nodes depict spin bundle representations of SO(1,9). An analog of Breitenlohner's approach is implemented to scan for superfields that contain graviton(s) and gravitino(s), which are the candidates for the prepotential superfields of 10D off-shell supergravity theories and separately abelian Yang-Mills theories are similarly treated. Version three contains additional content, both historical and conceptual, which broaden the reach of the scan in the 10D Yang-Mills case.