# String theory on the Schrodinger pp-wave background

## TL;DR

This paper investigates string theory on a specific pp-wave background derived from a non-supersymmetric Schrodinger geometry, solving for excitations and proposing an exact magnon dispersion relation.

## Contribution

It provides the first spectrum analysis of string excitations in this background and conjectures an exact dispersion relation for magnons in the original Schrodinger setting.

## Key findings

- Spectrum of bosonic excitations matches giant magnon dispersion.
- The background admits 16 Killing spinors and a Newton-Hooke type algebra.
- Proposes an exact magnon dispersion relation in the original background.

## Abstract

We study string theory on the pp-wave geometry obtained by taking the Penrose limit around a certain null geodesic of the non-supersymmetric Schrodinger background. We solve for the spectrum of bosonic excitations and find compelling agreement with the dispersion relation of the giant magnons in the Schrodinger background obtained previously in arXiv:1712.03091. Inspired by the pp-wave spectrum we conjecture an exact in the t'Hooft coupling dispersion relation for the magnons in the original Schrodinger background. We show that the pp-wave background admits exactly 16 Killing spinors. We use the explicit form of the latter in order to derive the supersymmetry algebra of the background which explicitly depends on the deformation parameter. Its bosonic subalgebra is of the Newton-Hooke type.