Alleviating the non-ultralocality of the AdS_5 x S^5 superstring

TL;DR

This paper extends the Faddeev-Reshetikhin procedure to the AdS_5 x S^5 superstring, modifying the Poisson bracket to address non-ultralocality and enabling lattice algebra formulation, connecting to Pohlmeyer reduction and sine-Gordon theory.

Contribution

It introduces a modified Poisson bracket for the AdS_5 x S^5 superstring that alleviates non-ultralocality, facilitating lattice algebra construction and linking to Pohlmeyer reduction.

Findings

Modified Poisson bracket alleviates non-ultralocality.

Lattice algebra matches that of the semi-symmetric space sine-Gordon theory.

Pohlmeyer reduction dynamics are reproduced with the new bracket.

Abstract

We generalize the initial steps of the Faddeev-Reshetikhin procedure to the AdS_5 x S^5 superstring theory. Specifically, we propose a modification of the Poisson bracket whose alleviated non-ultralocality enables to write down a lattice algebra for the Lax matrix. We then show that the dynamics of the Pohlmeyer reduction of the AdS_5 x S^5 superstring can be naturally reproduced with respect to this modified Poisson bracket. This work generalizes the alleviation procedure recently developed for symmetric space sigma-models. It also shows that the lattice algebra recently obtained for the AdS_5 x S^5 semi-symmetric space sine-Gordon theory coincides with the one obtained by the alleviation procedure.