A Perspective on Classical Strings from Complex Sine-Gordon Solitons

TL;DR

This paper explores classical string solutions with large spins on R x S^3 in AdS_5 x S^5, connecting them to Complex sine-Gordon solitons, and provides analytic profiles that interpolate between known string configurations.

Contribution

It introduces a unified framework linking classical string solutions to Complex sine-Gordon solitons, deriving analytic profiles that interpolate between different known string states.

Findings

Derived analytic string profiles from Lame and Complex sine-Gordon equations.

Showed the solutions interpolate between folded/circular strings and dyonic giant magnons.

Connected classical string solutions with integrable soliton models.

Abstract

We study a family of classical string solutions with large spins on R x S^3 subspace of AdS_5 x S^5 background, which are related to Complex sine-Gordon solitons via Pohlmeyer's reduction. The equations of motion for the classical strings are cast into Lame equations and Complex sine-Gordon equations. We solve them under periodic boundary conditions, and obtain analytic profiles for the closed strings. They interpolate two kinds of known rigid configurations with two spins: on one hand, they reduce to folded or circular spinning/rotating strings in the limit where a soliton velocity goes to zero, while on the other hand, the dyonic giant magnons are reproduced in the limit where the period of a kink-array goes to infinity.