Speeding Strings

Abstract

There is a class of single trace operators in $\mathcal{N}=4$ Yang-Mills theory which are related by the AdS/CFT correspondence to classical string solutions. Interesting examples of such solutions corresponding to periodic trajectories of the Neumann system were studied recently. In our paper we study a generalization of these solutions. We consider strings moving with large velocities. We show that the worldsheet of the fast moving string can be considered as a perturbation of the degenerate worldsheet, with the small parameter being the relativistic factor $\sqrt{1-v^2}$. The series expansion in this relativistic factor should correspond to the perturbative expansion in the dual Yang-Mills theory. The operators minimizing the anomalous dimension in the sector with given charges correspond to periodic trajectories in the mechanical system which is closely related to the product of two Neumann systems.

v3: added a reference to the earlier work

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• Spinning strings and AdS/CFT duality
• Semiclassical relativistic strings in S^5 and long coherent operators in N=4 SYM theory
• Large spin limits of AdS/CFT and generalized Landau-Lifshitz equations
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• On the tensionless limit of gauged WZW models
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• Supersymmetric null-surfaces
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• The SU(2) sector in AdS/CFT
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• Baecklund transformations, energy shift and the plane wave limit
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• Anomalous dimension and local charges
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• Spin chain from membrane and the Neumann-Rosochatius integrable system
• Elliptic String Solutions on RxS^2 and Their Pohlmeyer Reduction
• The SU(1|2) and SU(2|2) Sectors from Superstrings in AdS5 x S5