Pulsating strings in $Schr_5 \times T^{1,1}$ background

TL;DR

This paper investigates pulsating string solutions in a Schr"odinger $AdS_5 imes T^{1,1}$ background to explore non-relativistic holography and compute anomalous dimensions in the dual dipole CFT.

Contribution

It presents new pulsating string solutions in Schr"odinger backgrounds and semi-classical quantization, linking string energy corrections to operator dimensions in the dual field theory.

Findings

Derived specific pulsating string solutions in Schr"odinger space.

Quantized the solutions semi-classically and computed energy corrections.

Connected energy corrections to anomalous dimensions in the dual dipole CFT.

Abstract

The quest for extension of holographic correspondence to non-relativistic sectors naturally includes Schr\"odinger backgrounds and their field theory duals. In this paper we study the holography by probing the correspondence with pulsating strings. The case we consider is pulsating strings in five-dimensional Schr\"odinger space times five-torus $T^{1,1}$, which has as field theory dual a dipole CFT. First we find particular pulsating string solutions and then semi-classically quantize the theory. We obtain the wave function of the problem and thoroughly study the corrections to the energy, which by duality are supposed to give anomalous dimensions of certain operators in the dipole CFT.