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arXiv 0804.3301hep-th
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对旋转弦和缠绕状态的尺寸修正

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

Davide Astolfi, Gianluca Grignani, Troels Harmark, Marta Orselli

备注：
v2: 33 pages, misprints corrected, references added, version accepted for publication in JHEP
发表信息：
JHEP 0808:099,2008
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摘要：

我们计算了AdS_5 × S^5上圆旋转弦的能量、AdS_5 × S^5/Z_M上圆旋转弦的轨道推广的能量以及当J ->无穷大且J/M^2保持不变时作为轨道折叠圆弦解的极限的缠绕态的能量的高阶有限尺寸修正。我们在λ = λ/J^2的一阶上求解Bethe方程，其中λ是t Hooft耦合，Bethe方程描述了相应规范对偶算符在m/K展开式中的反常维数，其中m是缠绕数，K是“磁振子数”，对于圆形旋转弦和缠绕状态的解可以与从有效量子计算的能量相匹配。对于圆旋转弦在m^2和m^4中的前导1/J修正以及对m^2项的次前导1/J^2修正，我们发现一致。对于缠绕态，我们将能量完全匹配到1/J^2阶有限尺寸修正。对应于自旋闭弦的贝特方程的解也以m/K和J的所有阶展开式给出。

英文摘要：

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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