Integrability and Canonical Structure of d=2, N=16 Supergravity

TL;DR

This paper develops the canonical formulation of d=2, N=16 supergravity, revealing its symmetry algebra, conserved charges, and their algebraic structure, which enhances understanding of its integrability and symmetry properties.

Contribution

It provides the first detailed canonical formulation including supersymmetry generators and constructs conserved non-local charges related to affine E_9 symmetry.

Findings

Conserved charges commute with all constraints.

Charges form a Yangian algebra.

Explicit E_9 action on solutions.

Abstract

The canonical formulation of d=2, N=16 supergravity is presented. We work out the supersymmetry generators (including all higher order spinor terms) and the N=16 superconformal constraint algebra. We then describe the construction of the conserved non-local charges associated with the affine E_9 symmetry of the classical equations of motion. These charges are shown to commute weakly with the supersymmetry constraints, and hence with all other constraints. Under commutation, they close into a quadratic algebra of Yangian type, which is formally the same as that of the bosonic theory. The Lie-Poisson action of E_9 on the classical solutions is exhibited explicitly. Further implications of our results are discussed.