Finite-size Effects for Single Spike

TL;DR

This paper maps finite-size string solutions in R_t x S^3 to the complex sine-Gordon model, analyzing finite-size effects of single spike solutions and their energy-angle relations.

Contribution

It introduces a mapping between string solutions on R_t x S^3 and the complex sine-Gordon model, providing new finite-size solutions and effects analysis.

Findings

Finite-size string solutions are obtained and mapped to sine-Gordon solutions.

Leading finite-size effects of the single spike energy-angle relation are derived.

Results apply to both R_t x S^2 and R_t x S^3 geometries.

Abstract

We use the reduction of the string dynamics on R_t x S^3 to the Neumann-Rosochatius integrable system to map all string solutions described by this dynamical system onto solutions of the complex sine-Gordon integrable model. This mapping relates the parameters in the solutions on both sides of the correspondence. In the framework of this approach, we find finite-size string solutions, their images in the (complex) sine-Gordon system, and the leading finite-size effects of the single spike "E-\Delta\phi" relation for both R_t x S^2 and R_t x S^3 cases.