Spin chains and classical strings in two parameters $q$-deformed AdS$_3\times$S$^3$

TL;DR

This paper investigates the properties of spin chains and classical string solutions in a two-parameter q-deformed AdS3×S3 background, revealing new insights into their dispersion relations, string configurations, and pp-wave limits.

Contribution

It introduces a deformed spin chain model at the fast spin limit and analyzes giant magnons, hanging strings, and pp-wave limits in the two-parameter q-deformed setting.

Findings

Derived the deformed spin chain model at the fast spin limit.

Analyzed giant magnons and obtained their dispersion relations perturbatively.

Explored hanging string solutions and their charges numerically.

Abstract

In this paper, we study the spin chain and string excitation in the two-parameters $q$-deformed AdS$_3\times$S$^3$ proposed by Hoare. We obtain the deformed spin chain model at the fast spin limit for choices of deformed parameters. General ansatz for giant magnons are studied in great detail and complicated dispersion relation is treated perturbatively. We also study several types of hanging string solutions and their charges and spins are analyzed numerically. At last, we explore its pp-wave limit and find its solution only depends on the difference of deformed parameters.