On the pulsating strings in Sasaki-Einstein spaces

TL;DR

This paper explores pulsating string solutions in specific Sasaki-Einstein spaces, deriving new solutions with Heun functions, but faces challenges in quantization and calculating energy corrections relevant for dual gauge theories.

Contribution

It introduces a generalized ansatz for pulsating strings in AdS_5 x Y^{p,q} and L^{p,q,r} spaces, finding new solutions involving Heun functions and extending previous analyses.

Findings

Derived new pulsating string solutions in Sasaki-Einstein spaces.

Expressed solutions in terms of Heun functions, highlighting mathematical complexity.

Identified limitations in quantizing solutions and computing energy corrections.

Abstract

We study the class of pulsating strings in AdS_5 x Y^{p,q} and AdS_5 x L^{p,q,r}. Using a generalized ansatz for pulsating string configurations, we find new solutions for this class in terms of Heun functions, and derive the particular case of AdS_5 x T^{1,1}, which was analyzed in arXiv:1006.1539 [hep-th]. Unfortunately, Heun functions are still little studied, and we are not able to quantize the theory quasi-classically and obtain the first corrections to the energy. The latter, due to AdS/CFT correspondence, is supposed to give the anomalous dimensions of operators of the gauge theory dual N=1 superconformal field theory.