Supersymmetry algebras and Lorentz invariance for d=10 Super Yang-Mills

TL;DR

This paper explores embedding conventional supersymmetry into a broader framework for 10-dimensional super Yang-Mills, revealing various closed supersymmetry algebras with different invariance groups and auxiliary field transformations.

Contribution

It introduces new solutions for embedding supersymmetry in 10D super Yang-Mills with diverse invariance groups and auxiliary field behaviors, extending previous methods.

Findings

Identified supersymmetry solutions with different invariance groups.

Reproduced known auxiliary field additions for superalgebra closure.

Showed auxiliary fields can transform non-trivially under Lorentz symmetry.

Abstract

We consider ways in which conventional supersymmetry can be embedded in the set of more general fermionic transformations proposed recently [\Ref{B}] as a framework in which to study $d=10$ super Yang-Mills. Solutions are exhibited which involve closed algebras of various numbers of supersymmetries together with their invariance groups: nine supersymmetries with $\GT {\times}\SO (1,1)$ invariance; eight supersymmetries with $\SO (7){\times}\SO (1,1)$ invariance; four supersymmetries with $\SO (3,1){\times}\U (3)$ invariance. We recover in this manner all previously known ways of adding finite numbers of bosonic auxiliary fields so as to partially close the $d=10$ superalgebra. A crucial feature of these solutions is that the auxiliary fields transform non-trivially under the residual Lorentz symmetry, even though they are originally introduced as Lorentz scalars.