Massive (p,q)-supersymmetric sigma models revisited

TL;DR

This paper analyzes the algebraic structure and symmetry properties of massive (p,q)-supersymmetric sigma models in two dimensions, revealing unexpected automorphism group characteristics and reexamining supersymmetry conditions.

Contribution

It computes the Poisson bracket algebra of supersymmetry and central charges, and shows the automorphism group is a subgroup of SO(3) for (4,4) models, revisiting supersymmetry conditions without prior assumptions.

Findings

Poisson bracket algebra of supersymmetry charges derived

Automorphism group for (4,4) models is a subgroup of SO(3)

Reanalysis of supersymmetry conditions for zero torsion models

Abstract

We recently obtained the conditions on the couplings of the general two-dimensional massive sigma-model required by (p,q)-supersymmetry. Here we compute the Poisson bracket algebra of the supersymmetry and central Noether charges, and show that the action is invariant under the automorphism group of this algebra. Surprisingly, for the (4,4) case the automorphism group is always a subgroup of SO(3), rather than SO(4). We also reanalyse the conditions for the (2,2) and (4,4) supersymmetry of the zero torsion models without assumptions about the central charge matrix.