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Spinning strings and AdS/CFT duality

A. A. Tseytlin

TL;DR

The paper surveys a class of semiclassical strings in AdS_5 × S^5 whose energies admit a regular expansion in ${\lambda \over J^2}$, enabling direct tests of AdS/CFT in non-supersymmetric sectors. By exploiting an Rt × S^5 sigma-model reduction to the Neumann/Neumann-Rosochatius integrable systems, it derives energy–spin relations for circular and folded multi-spin strings and analyzes their stability and 1-loop corrections. The results show how integrable structures provide a bridge between classical string dynamics and perturbative SYM via spin-chain techniques, supporting the duality in non-BPS settings and suggesting universality in the large-J limit. The work also identifies open questions, such as a complete classification of regular-expansion solutions and the extension to less supersymmetric backgrounds, with pulsating and mixed-AdS/S^5 configurations as promising directions.

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.

Spinning strings and AdS/CFT duality

TL;DR

The paper surveys a class of semiclassical strings in AdS_5 × S^5 whose energies admit a regular expansion in , enabling direct tests of AdS/CFT in non-supersymmetric sectors. By exploiting an Rt × S^5 sigma-model reduction to the Neumann/Neumann-Rosochatius integrable systems, it derives energy–spin relations for circular and folded multi-spin strings and analyzes their stability and 1-loop corrections. The results show how integrable structures provide a bridge between classical string dynamics and perturbative SYM via spin-chain techniques, supporting the duality in non-BPS settings and suggesting universality in the large-J limit. The work also identifies open questions, such as a complete classification of regular-expansion solutions and the extension to less supersymmetric backgrounds, with pulsating and mixed-AdS/S^5 configurations as promising directions.

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.

Paper Structure

This paper contains 22 sections, 202 equations.

Table of Contents

  1. Introduction
  2. Closed superstrings in $AdS_5 \times S^5$: classical solutions
  3. $R_t \times S^5$ sigma model : classical integrability and conserved charges
  4. Reduction of $R_t \times S^5$ sigma-model to 1-d Neumann system
  5. Rotating string ansatz
  6. Integrals of motion and constraints
  7. Special case of $n=3$ Neumann system
  8. Types of solutions and rotating strings in flat space
  9. Simplest circular solutions in $R_t \times S^5$: $\Lambda={\rm const}$
  10. Constant radii solution
  11. Energy as function of spins
  12. Quadratic fluctuations near circular solutions
  13. 1-loop string correction to the classical energy
  14. Rotating strings in $AdS_5 \times S^5\ $
  15. Simple circular strings in $AdS_5$
  16. ...and 7 more sections