Review of AdS/CFT Integrability, Chapter III.1: Bethe Ansatze and the R-Matrix Formalism

被引：10

作者：

Staudacher, Matthias ^{[1
,2
,3
]}

机构：

[1] Humboldt Univ, Inst Math, D-12489 Berlin, Germany

[2] Humboldt Univ, Inst Phys, D-12489 Berlin, Germany

[3] Albert Einstein Inst, Max Planck Inst Gravitat Phys, D-14476 Potsdam, Germany

来源：

LETTERS IN MATHEMATICAL PHYSICS | 2012年 / 99卷 / 1-3期

关键词：

Bethe ansatz; R-matrix; Q-operator;

D O I：

10.1007/s11005-011-0530-9

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

The one-dimensional Heisenberg XXX spin chain appears in a special limit of the AdS/CFT integrable system. We review various ways of proving its integrability, and discuss the associated methods of solution. In particular, we outline the coordinate and the algebraic Bethe ansatz, giving reference to literature suitable for learning these techniques. Finally, we speculate which of the methods might lift to the exact solution of the AdS/CFT system, and sketch a promising method for constructing the Baxter Q-operator of the XXX chain. It allows to find the spectrum of the model using certain algebraic techniques, while entirely avoiding Bethe's ansatz.

引用

页码：191 / 208

页数：18

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