arXiv 1206.40612012-06hep-th

可积系统与AdS/CFT对偶

Integrable systems and AdS/CFT duality

Sebastien Leurent

备注：: PhD thesis : 275 pages, including 10 introductory pages in french at the begining (repeated afterwards in english) v2 : typos fixed and five references added

摘要：

这篇博士论文探讨了可积自旋链和量子场论之间的相似之处，如超级杨米尔斯。我们首先研究可积自旋链，并明确地建立一个多项式的“Backlund流”和多项式的“Q-算子”，允许对角化的哈密顿量。然后，我们研究可积场论等显示如何获得“Q-功能”，类似于Q-运营商建立自旋链。结果表明，这些Q -函数的解析性质中包含了一些重要的信息.这使得获得，在热力学贝特anterior的框架中，有限数量的非线性积分方程编码的有限大小的频谱的理论，我们研究。这个方程组等价于最近在AdS/CFT对偶的情况下得到的一个称为“Y-系统”的无限方程组。

英文摘要：

This PhD thesis explores the similarities between integrable spin chains and quantum field theories, such as Super Yang Mills. We first study integrable spin chains and build explicitly a polynomial "Backlund flow" and polynomial "Q-operators", which allow to diagonalize the Hamiltonian. We then study integrable field theories et show how to obtain "Q-functions", analogous to the Q-operators built for spin chains. It turns out that several important informations are contained in the analytic properties of these Q -functions. That allows to obtain, in the framework of the thermodynamic Bethe ansatz, a finite number of non-linear integral equations encoding the finite-size spectrum of the theory which we study. This system of equations is equivalent to an infinite system of equations, known as "Y-system", which had been quite recently conjectured in the case of the AdS/CFT duality.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

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