[Paper Review] Spinning strings and AdS/CFT duality

A.A. Tseytlin|ArXiv.org|Nov 17, 2003

Black Holes and Theoretical PhysicsPhysics and Astronomy81 references170 citations

TL;DR

This paper investigates semiclassical spinning string states in $AdS_5\times S^5$ to test the AdS/CFT duality beyond BPS states. By analyzing rotating and pulsating string solutions with large quantum numbers, it shows that the string energy expands regularly in $\lambda/J^2$, enabling quantitative comparison with gauge theory scaling dimensions and revealing integrable structures on both sides of the duality.

ABSTRACT

We review a special class of semiclassical string states in AdS_5 x S^5 which have a regular expansion of their energy in integer powers of the ratio of the square of string tension (`t Hooft coupling) and the square of large angular momentum in S^5. They allow one to quantitatively check the AdS/CFT duality in non-supersymmetric sector of states and also help to uncover the role of integrable structures on the two sides of the string theory -- gauge theory duality.

Motivation & Objective

• To test the AdS/CFT duality in non-supersymmetric sectors by studying semiclassical string states with large quantum numbers.
• To explore the emergence of integrable structures in both the string sigma model and the planar $\mathcal{N}=4$ SYM theory.
• To establish a quantitative match between string energy expansions and gauge theory anomalous dimensions in the large spin limit.
• To generalize the BMN correspondence to multispin string solutions and analyze their 1-loop corrections.
• To investigate the role of the Neumann-Rosochatius system in describing rotating and pulsating string solutions in $AdS_5\times S^5$.

Proposed method

• Analyzes classical rotating string solutions in $AdS_5\times S^5$ using a rotating string ansatz with large angular momentum $J$ in $S^5$.
• Reduces the $R_t \times S^5$ sigma model to a 1D Neumann system via constraints and conserved charges, enabling integrable dynamics.
• Derives the effective 1D Lagrangian for the Neumann system, including terms for radial motion, angular momenta $\mathcal{J}_i$, and a Lagrange multiplier $\Lambda$.
• Computes the classical energy as a function of spins and analyzes quadratic fluctuations around circular string solutions to extract 1-loop corrections.
• Applies the $J \to \infty$ limit with $\lambda/J^2$ fixed to suppress higher-order string corrections, enabling comparison with perturbative gauge theory.
• Studies pulsating string solutions with three $S^5$ spins $\mathcal{J}_i$, showing regular expansion in $\lambda/N^2$ where $N$ is the oscillation level number.

Experimental results

Research questions

• RQ1 Can semiclassical spinning string states in $AdS_5\times S^5$ provide a quantitative test of the AdS/CFT duality beyond BPS states?
• RQ2 Do the energy expansions of multispin string solutions in the $J \to \infty$, $\lambda/J^2$ fixed limit match the perturbative gauge theory scaling dimensions?
• RQ3 What is the role of integrable structures, such as the Neumann-Rosochatius system, in connecting string theory and gauge theory dynamics?
• RQ4 Are 1-loop string corrections suppressed in the large $J$ limit for non-BPS spinning strings, enabling reliable comparison with gauge theory?
• RQ5 Can pulsating string solutions with multiple spins exhibit regular expansions in $\lambda/N^2$, and can they be matched to anomalous dimensions in $\mathcal{N}=4$ SYM?

Key findings

• The energy of rotating strings with large $J$ in $S^5$ admits a regular expansion in powers of $\lambda/J^2$, enabling quantitative comparison with gauge theory.
• For circular two-spin solutions, the classical energy is $E = J + f(\lambda)\ln J + \cdots$, with $f(\lambda)$ matching the anomalous dimension function in $\mathcal{N}=4$ SYM at weak coupling.
• The 1-loop string correction to the classical energy is suppressed in the $J \to \infty$ limit, allowing reliable comparison with perturbative gauge theory results.
• Pulsating string solutions with three $S^5$ spins are described by a Neumann-Rosochatius system and exhibit a regular expansion in $\lambda/N^2$, with the leading term matching a specific anomalous dimension in SYM.
• The emergence of the same integrable structure (Neumann-Rosochatius system) on both the string and gauge theory sides suggests a deeper duality between the effective sigma model and spin chain Hamiltonians.
• The results support the idea that integrable structures in the planar $\mathcal{N}=4$ SYM theory and in the string sigma model are manifestations of the same underlying symmetry, even in non-supersymmetric sectors.