In this introductory review we discuss dynamical tests of the AdS5 × S5 string/ Super Yang-Mills duality. After a brief introduction to AdS/CFT, we argue that semiclassical string energies yield information on the quantum spectrum of the string in the limit of large angular momenta on the S5. The energies of the folded and circular spinning string solutions rotating on a S3 within the S5 are derived, which yield all-loop predictions for the dual gauge theory scaling dimensions. These follow from the eigenvalues of the dilatation operator of Super Yang-Mills in a minimal SU(2) subsector, and we display its reformulation in terms of a Heisenberg s = 1/2 spin chain along with the coordinate Bethe ansatz for its explicit diagonalization. In order to make contact to the spinning string energies, we then study the thermodynamic limit of the one-loop gauge theory Bethe equations and demonstrate the matching with the folded and closed string result at this loop order. Finally, the known gauge theory results at higher-loop orders are reviewed and the associated long-range spin chain Bethe ansatz is introduced, leading to an asymptotic all-loop conjecture for the gauge theory Bethe equations. This uncovers discrepancies at the three-loop order between gauge theory scaling dimensions and string theory energies and the implications of this are discussed. Along the way, we comment on further developments and generalizations of the subject and point to the relevant literature.
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机译：在这篇介绍性综述中，我们讨论了AdS5×S 5 字符串/ Super Yang-Mills对偶性的动态测试。在简要介绍AdS / CFT之后，我们认为，半经典弦能量在S 5 的大角动量极限内在弦的量子谱上产生信息。得出在S 5 内在S 3 上旋转的折叠和圆形纺丝线溶液的能量，从而得出双轨距理论定标尺寸的全回路预测。这些遵循Super Yang-Mills扩张算子在最小SU（2）子部门中的特征值，我们根据Heisenberg s = 1/2自旋链以及坐标Bethe ansatz对其显式对角化显示其重新表示形式。为了与纺丝线能量接触，我们接着研究了单圈规理论Bethe方程的热力学极限，并证明了在这种循环顺序下与折叠和闭合丝线结果的匹配。最后，对已知的高环阶规范理论结果进行了综述，并引入了相关的远程自旋链Bethe ansatz，从而导致了规范理论Bethe方程的渐近全环猜想。这揭示了规范理论定标尺寸与弦理论能量之间的三环级差异，并对此进行了讨论。在此过程中，我们评论了该主题的进一步发展和概括，并指出了相关文献。
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