3 Dimensional N=8 Supersymmetric Field Theory Revisited

TL;DR

This paper revisits 3D N=8 supersymmetric field theories, proposing models based on non-associative algebraic structures that exhibit specific symmetry groups and degrees of freedom scaling.

Contribution

It introduces new 3D N=8 SUSY theories using non-associative algebra ideas, detailing their symmetry properties and degrees of freedom scaling.

Findings

Theories represent subalgebras of OSp(8|2) and OSp(8|4).

Degrees of freedom scale as N^{3/2}.

Existence of an extra permutation symmetry group.

Abstract

Inspired by ideas regarding Hermitian NxN matrix fields obeying a non-associative algebra, 3-dimensional N=8 SUSic field theories are proposed to on-shell represent subalgebras of OSp(8|2) and OSp(8|4) groups of SUSY transformations. They are theories of 8 scalar and 8 spinor fields with Yukawa, quartic and sextic self-interactions. The actions as their R-symmetry exhibit only SO(7) or SO(4)xSO(4) subgroups of full SO(8) automorphisms. It is argued that the number of degrees of freedom scale like N^{3/2}. There also exists an extra S_N permutation symmetry group.