Semiclassical spectrum for BMN string in $Sch_5\times S^5$

TL;DR

This paper computes the semiclassical spectrum of BMN strings in a Schrödinger spacetime using algebraic curves and compares it with anomalous dimensions in a deformed super Yang-Mills theory, advancing understanding of integrable structures.

Contribution

It introduces a method to derive the semiclassical spectrum for strings in Schrödinger spacetime and compares it with gauge theory results, highlighting integrability in deformed backgrounds.

Findings

Semiclassical spectrum matches anomalous dimensions in the deformed gauge theory.

Algebraic curve method effectively computes spectra in Schrödinger backgrounds.

Results support integrability of string theory in $Sch_5\times S^5$.

Abstract

We investigate the algebraic curve for string in $Sch_5\times S^5$. We compute the semiclassical spectrum for BMN string in $Sch_5\times S^5$ from the algebraic curve. We compare our results with the anomalous dimensions in $sl(2)$ sector of the null dipole deformation of $\mathcal{N} = 4$ super Yang-Mills theory.