Finite size effects in classical string solutions of the Schrodinger geometry

TL;DR

This paper investigates finite size effects on classical string solutions in Schrodinger spacetime, deriving exponential corrections to dispersion relations and analyzing their behavior in various limits.

Contribution

It provides the first detailed computation of finite size corrections for giant magnon and spike solutions in Schrodinger geometry, extending known results from AdS/CFT.

Findings

Finite size corrections are exponential in the size of the string.

In the zero deformation limit, results reduce to AdS5×S5 cases.

Infinite size limit reproduces known dispersion relations.

Abstract

We study finite size corrections to the semiclassical string solutions of the Schrodinger spacetime. We compute the leading order exponential corrections to the infinite size dispersion relation of the single spin giant magnon and of the single spin single spike solutions. The solutions live in a $S^3$ subspace of the five-sphere and extent in the Schrodinger part of the metric. In the limit of zero deformation the finite size dispersion relations flow to the undeformed $AdS_5 \times S^5$ counterparts and in the infinite size limit the correction term vanishes and the known infinite size dispersion relations are obtained.