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arXiv 0906.2546hep-th
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AdS/CFT的离散Hirota动力学

Discrete Hirota dynamics for AdS/CFT

Arpad Hegedus

摘要:

最近,在平面N=4超对称Yang-Mills理论中,给出了一组定义任意局部单迹算子反常维数的函数方程.这些函数方程采用在特殊形状区域上定义的Y系统的形式。这个Y系统可以等效地重新表述为定义在“T形脂肪钩”上的T系统。T-系统的元素满足离散Hirota方程。本文通过一系列Backlund变换求解AdS/CFT的离散Hirota方程,得到了AdS/CFT的TT-、TQ-和QQ-关系。

英文摘要:

Recently a set of functional equations defining the anomalous dimensions of arbitrary local single trace operators in planar N=4 supersymmetric Yang-Mills theory has been conjectured. These functional equations take the form of a Y-system defined on a special shaped domain. This Y-system can be equivalently reformulated as a T-system defined on a "T-shaped fat hook". The elements of the T-system satisfy discrete Hirota equations. In the present paper the discrete Hirota equations for AdS/CFT are solved by means of a chain of Backlund transformations and as a result TT-, TQ-, and QQ-relations are obtained for AdS/CFT.

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