Generalized pulsating strings

TL;DR

The paper addresses generalizing pulsating strings in $AdS_5\times S^5$ by employing a generalized ansatz that leads to a constrained $SO(6)$ sigma-model with a Lagrange multiplier $\Lambda$. It finds two regimes of classical solutions—harmonic for constant $\Lambda$ and Jacobi-elliptic for non-constant $\Lambda$—and uses a Minahan-inspired semiclassical quantization to compute the leading energy correction $E^{2}_{(1)}$ via a perturbative integral involving the $S^5$ and $S^3$ wavefunctions. The results yield novel expressions for the anomalous dimensions that differ significantly from previous works due to the distinct classical solutions. This work deepens the AdS/CFT correspondence by providing new spectral data for highly excited, non-BPS-like pulsating strings and motivates future Bethe-ansatz analyses on the SYM side.

Abstract

In this paper we consider new solutions for pulsating strings. For this purpose we use tha idea of the generalized ansatz for folded and circular strings in hep-th/0311004. We find the solutions to the resulting Neumann-Rosochatius integrable system and the corrections to the energy. To do that we use the approach developed by Minahan in hep-th/0209047 and find that the corrections are quite different from those obtained in that paper and hep-th/0310188. We conclude with comments on our solutions and obtained corrections to the energy, expanded to the leading order in lambda.