Solvable Iattice models associated with supera I gebras and related topics

与超代数及相关主题相关的可解格子模型

• 批准号: 19740244
• 负责人: TSUBOI Zengo
• 金额: $ 2.39万
• 依托单位: Okayama Institute for Quantum Physics
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (B)
• 财政年份: 2007
• 资助国家: 日本
• 起止时间: 2007 至 2010
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-19740244/
• 关键词: 数理物理; 可解模型; ベーテ仮説; AdS; CFT対応; superalgebra; 表現論; 統計力学; 可積分系; AdS/CFT対応; ソリトン; べーテ仮説; 表現諭; ベーテ仮説法; Baxter Q-operator; q-supercharacter; 可解格子膜型; Baxter Q演算子

We have researched on the following topics on integrable models related to superalgebras. We have constructed the Baxter Q-operators for Uq(sl(2 11)1), functional relations among them and Wronskian-type expressions of T-operators (transfer matrices). Our formulation can be applicable to both lattice models and conformal field theory since it is independent of the space where the operators act on.I made non-trivial generalization of Wronskian-type formulae to Uq(gl(M I N)A) case, and gave Wronskian-type solutions of the T-system. They are yet another form of the so-called q-(super)characters. I identified that the number of the Baxter Q-operators is 2A{M+N} for the first time.Based on the technique developed through the above research, we gave solutions to the T-and Q-systems for the AdS/CFT in particle physics.We proposed a new definition of the 2A{M+N} Baxter Q-operators based on 'co-derivative' on generating functions of supercharacters of gl(M I N), and derived the Bethe ansatz equations without using the Bethe ansatz. We also clarified relations between Backlund transformations in the soliton theory and the Baxter Q-operators on the level of operator.

我们在与超代数相关的可积模型方面进行了以下研究。我们构造了Uq(sl(2，11)1)的Baxter Q-算子，它们之间的函数关系以及T-算子(转移矩阵)的Wronskian形式。我们的公式既适用于格子模型，也适用于共形场理论，因为它与算符作用的空间无关。我将Wronskian公式非平凡地推广到Uq(gl(M，I，N)A)的情形，给出了T系统的Wronskian解。它们是所谓Q-(超级)字的另一种形式。在此基础上，给出了粒子物理中ADS/CFT的T-系统和Q-系统的求解方法，提出了一种新的基于gl(M，I，N)的超标生成函数的上导数的新定义，并在不使用Bethe ansatz的情况下，推导出了Bethe ansatz方程。我们还阐明了孤子理论中的Backlund变换与算符水平上的Baxter Q-算子之间的关系。

项目成果

Baxter Q-operators for quantum affine superalgebras(ポスター発表)

量子仿射超代数的 Baxter Q 算子（海报展示）

• 发表时间: 2007
• 作者: 坪井 禅吾;V.Bazhanov;Zengo Tsuboi;Zengo Tsuboi;坪井 禅吾;Zengo Tsuboi;坪井 禅吾;坪井 禅吾
• 通讯作者: 坪井 禅吾

PSU(2, 2|4) Character of Quasiclassical AdS/CFT

PSU(2, 2|4) 准经典 AdS/CFT 的特征

• 发表时间: 2010
• 期刊: Journal of High Energy Physics
• 影响因子: 5.4
• 作者: Nikolay Gromov;Vladimir Kazakov;Zengo Tsuboi
• 通讯作者: Zengo Tsuboi

Baxter's Q-operators for supersymmetric spin chains

超对称自旋链的 Baxter Q 算子

• 发表时间: 2008
• 期刊: Nuclear Physics B805[FS]
• 作者: Vladimir V.;Bazhanov;Zengo Tsuboi
• 通讯作者: Zengo Tsuboi

Solutions of the T-system and Baxter equations for supersymmetric spin chains

超对称自旋链的 T 系统和 Baxter 方程的解

• 发表时间: 2009
• 作者: Vladimir V.Bazhanov;Zengo Tsuboi;Zengo Tsuboi;坪井禅吾;Zengo Tsuboi;Zengo Tsuboi
• 通讯作者: Zengo Tsuboi

Baxter Q-operators for U_{q}(hat[sl](2|1))

U_{q}(hat[sl](2|1)) 的 Baxter Q 算子

• 发表时间: 2007
• 作者: 坪井 禅吾;V.Bazhanov;Zengo Tsuboi;Zengo Tsuboi;坪井 禅吾;Zengo Tsuboi;坪井 禅吾
• 通讯作者: 坪井 禅吾