Anisotropic Landau-Lifshitz sigma models from q-deformed AdS_5 x S^5 superstrings

TL;DR

This paper derives and analyzes anisotropic Landau-Lifshitz sigma models from q-deformed AdS_5 x S^5 superstrings, revealing integrable structures, conserved charges, and quantum affine algebras in specific subsectors.

Contribution

It introduces new anisotropic Landau-Lifshitz sigma models from q-deformed superstrings and uncovers their integrable properties and algebraic structures.

Findings

Construction of infinite non-local conserved charges

Identification of quantum affine algebra at classical level

Discovery of Yangians via non-local gauge transformations

Abstract

We consider bosonic subsectors of the q-deformed AdS_5 x S^5 superstring action and study the classical integrable structure of anisotropic Landau-Lifshitz sigma models (LLSMs) derived by taking fast-moving limits. The subsectors are 1) deformed AdS_3 x S^1 and 2) R x deformed S^3. The cases 1) and 2) lead to a time-like warped SL(2) LLSM and a squashed S^3 LLSM, respectively. For each of them, we construct an infinite number of non-local conserved charges and show a quantum affine algebra at the classical level. Furthermore, a pp-wave like limit is applied for the case 1). The resulting system is a null-like warped SL(2) LLSM and exhibits a couple of Yangians through non-local gauge transformations associated with Jordanian twists.