A lattice Poisson algebra for the Pohlmeyer reduction of the AdS_5 x S^5 superstring

TL;DR

This paper derives the Poisson algebra for the Lax matrix in the Pohlmeyer reduction of the AdS_5 x S^5 superstring, revealing a manageable non-ultralocality that allows for a lattice formulation.

Contribution

It provides the first-principles derivation of the Poisson algebra and introduces a lattice Poisson algebra for this integrable superstring model.

Findings

Non-ultralocality is mild, facilitating lattice discretization.

Explicit lattice Poisson algebra is constructed.

Enhances understanding of integrable structures in superstring theory.

Abstract

The Poisson algebra of the Lax matrix associated with the Pohlmeyer reduction of the AdS_5 x S^5 superstring is computed from first principles. The resulting non-ultralocality is mild, which enables to write down a corresponding lattice Poisson algebra.