Higher-spin conserved currents in supersymmetric sigma models on symmetric spaces

TL;DR

This paper constructs and analyzes higher-spin conserved currents in supersymmetric sigma models on symmetric spaces, revealing their algebraic structure and potential implications for quantized theories.

Contribution

It introduces new classes of higher-spin conserved currents in supersymmetric sigma models on symmetric spaces and analyzes their algebraic properties.

Findings

Primitive currents form a basis for all conserved currents.

Bosonic charges commute under Poisson brackets.

Fermionic charges form a higher-spin supersymmetry algebra.

Abstract

Local higher-spin conserved currents are constructed in the supersymmetric sigma models with target manifolds symmetric spaces $G/H$. One class of currents is based on generators of the de Rham cohomology ring of $G/H$; a second class of currents are higher-spin generalizations of the (super)energy-momentum tensor. A comprehensive analysis of the invariant tensors required to construct these currents is given from two complimentary points of view, and sets of primitive currents are identified from which all others can be constructed as differential polynomials. The Poisson bracket algebra of the top component charges of the primitive currents is calculated. It is shown that one can choose the primitive currents so that the bosonic charges all Poisson-commute, while the fermionic charges obey an algebra which is a form of higher-spin generalization of supersymmetry. Brief comments are made on some implications for the quantized theories.