## Spinning strings in AdS(5) x S**5 and integrable systems

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**Citation: **

*G. Arutyunov, S. Frolov, J. Russo and A. A. Tseytlin, Spinning strings in AdS(5) x S**5 and integrable systems, Nuclear Physics B, 671, 3, 2003, 3-50*

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**Abstract: **

We show that solitonic solutions of the classical string action on the AdS5 ? S5
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 J1, J2.

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**Author's Homepage: **

http://people.tcd.ie/frolovs
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**Description: **

PUBLISHED
**Author:**FROLOV, SERGEY

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**Publisher: **

Elsevier
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**Type of material: **

Journal Article#####
**Series/Report no: **

Nuclear Physics B;671;

3;

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**Availability: **

Full text available#####
**Keywords: **

Mathematics, string theory
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