Finite-size corrections to the rotating string and the winding state

Details Finite-size corrections to the rotating string and the winding state Finite-size corrections to the rotating string and the winding state

2008-04-21

arxiv.org/abs/0804.3301v2

JHEP0808:099,2008

Physics

High Energy Physics

High Energy Physics - Theory

v2: 33 pages, misprints corrected, references added, version accepted for publication in JHEP

Scientific paper

10.1088/1126-6708/2008/08/099

We compute higher order finite size corrections to the energies of the circular rotating string on AdS_5 x S^5, of its orbifolded generalization on AdS_5 x S^5/Z_M and of the winding state which is obtained as the limit of the orbifolded circular string solution when J -> infinity and J/M^2 is kept fixed. We solve, at the first order in lambda'=lambda/J^2, where lambda is the 't Hooft coupling, the Bethe equations that describe the anomalous dimensions of the corresponding gauge dual operators in an expansion in m/K, where m is the winding number and K is the "magnon number", and to all orders in the angular momentum J. The solution for the circular rotating string and for the winding state can be matched to the energy computed from an effective quantum Landau-Lifshitz model beyond the first order correction in 1/J. For the leading 1/J corrections to the circular rotating string in m^2 and m^4 and for the subleading 1/J^2 corrections to the m^2 term, we find agreement. For the winding state we match the energy completely up to, and including, the order 1/J^2 finite-size corrections. The solution of the Bethe equations corresponding to the spinning closed string is also provided in an expansion in m/K and to all orders in J.

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