Finite Size Effect from Classical Strings in deformed AdS$_3\times$ S$^3$

TL;DR

This paper investigates how finite size influences classical string solutions in a deformed AdS3×S3 background, deriving exponential corrections to dispersion relations for giant magnons, single spikes, and spinning folded strings.

Contribution

It provides explicit calculations of finite size effects for various classical string solutions in a deformed AdS3×S3 space, including novel expressions involving Lambert W-functions.

Findings

Derived exponential corrections to giant magnon and single spike dispersion relations.

Expressed finite size effects for spinning folded strings using Lambert W-function.

Enhanced understanding of finite size effects in deformed AdS/CFT correspondence.

Abstract

We study the finite size effect of rigidly rotating and spinning folded strings in $(AdS_3\times S^3)_{\varkappa}$ background. We calculate the leading order exponential corrections to the infinite size dispersion relation of the giant magnon, and single spike solutions. For the spinning folded strings we write the finite size effect in terms of the known Lambert $W$-function.