Spinning strings in AdS_5 x S^5 and integrable systems

TL;DR

This paper connects classical spinning string solutions in AdS_5 x S^5 with integrable systems, deriving equations to compute their energies and anomalous dimensions, and identifies specific solutions matching SYM operator dimensions.

Contribution

It establishes a classification of spinning string solutions via the Neumann integrable system and derives equations for their energies, linking string theory to gauge theory anomalous dimensions.

Findings

Derived equations for string energy as a function of spins.

Identified a string solution matching one-loop anomalous dimensions.

Proposed a connection between classical string solutions and the thermodynamic limit of the Bethe ansatz.

Abstract

We show that solitonic solutions of the classical string action on the AdS_5 x S^5 background that carry charges (spins) of the Cartan subalgebra of the global symmetry group can be classified in terms of periodic solutions of the Neumann integrable system. We derive equations which determine the energy of these solitons as a function of spins. In the limit of large spins J, the first subleading 1/J coefficient in the expansion of the string energy is expected to be non-renormalised to all orders in the inverse string tension expansion and thus can be directly compared to the 1-loop anomalous dimensions of the corresponding composite operators in N=4 super YM theory. We obtain a closed system of equations that determines this subleading coefficient and, therefore, the 1-loop anomalous dimensions of the dual SYM operators. We expect that an equivalent system of equations should follow from the thermodynamic limit of the algebraic Bethe ansatz for the SO(6) spin chain derived from SYM theory. We also identify a particular string solution whose classical energy exactly reproduces the one-loop anomalous dimension of a certain set of SYM operators with two independent R charges J_1, J_2.