The $\mathcal {OSP}(2,2|16)$ superconformal theory is free!

TL;DR

This paper demonstrates that a specific three-dimensional superconformal theory with SO(16) symmetry and equal bosonic and fermionic content cannot support interactions, indicating it is inherently free.

Contribution

It provides a proof, using algebraic and covariant methods, that the $ ext{OSP}(2,2|16)$ superconformal theory in three dimensions is necessarily free and non-interacting.

Findings

The theory cannot sustain interactions due to algebraic constraints.

Light-cone superspace techniques show algebraic inconsistency.

Covariant methods using SO(16) Fierz identities fail to support interactions.

Abstract

The SuperConformal theory in three space-time dimensions with SO(16) $R$-symmetry, 128 bosons, and 128 fermions, cannot sustain interactions. This result is obtained using both light-cone superspace techniques which rely on algebraic consistency, and covariant methods which rely on SO(16) Fierz identities which fail to produce the desired algebra.