Quantum Algebras and Integrable Boundaries in AdS/CFT
Quantum Algebras and Integrable Boundaries in AdS/CFT
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AdS/CFT 中的量子代数和可积边界
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
V. Regelskis
中科院分区：
文献类型：
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作者：
V. Regelskis
本文研究了在ADS/CFT对偶中产生并受到其启发的量子可积结构，如Yangans和量子仿射代数，主要侧重于探索隐藏在对偶中的可积边界。本论文的主要目的是寻找新的代数结构和方法，为量子群理论和规范/引力对偶中边界效应的探索开辟新的天地。
这项工作的主要目的是探索ADS/CFT世界薄片散射理论和表现为DP-膜(p+1维Dirichlet子流形)的可积边界，这是超弦理论的必要部分。这些物体的存在破坏了一些基本的对称性，并导致了由体积对称性的上理想子代数支配的边界散射理论。详细讨论了D3膜、D5膜和D7膜的边界散射理论，揭示了D3膜、D5膜和D7膜的边界杨氏对称性。
ADS/CFT世界薄层散射理论与变形Hubbard链的散射理论密切相关。这种相似性允许我们将量子形变方法应用于边界散射理论。这种对系统的处理导致了量子仿射对称，它以一种非常优雅和紧凑的形式显现出来。通过这种方式，以前看起来彼此不相关的不同边界的对称性以统一和连贯的形式出现。
量子形变方法也有助于我们更好地理解所谓的秘密对称现象。它之所以被称为秘密，是因为它看起来像是该系统的阳年的一级生成器。然而，它没有李代数(零级)类比。这种对称性被证明起源于量子变形模型，在该模型中，它表现为相应的量子仿射代数的两个能级一级和负一级生成器。
This thesis studies quantum integrable structures such as Yangians and quantum affine algebras that arise in and are inspired by the AdS/CFT duality, with a primary emphasis on the exploration of integrable boundaries deeply hidden in the duality. The main goal of this thesis is to find novel algebraic structures and methods that could lead to new horizons in the theory of quantum groups and in the exploration of boundary effects in the gauge/gravity dualities.
The main thrust of this work is the exploration of the AdS/CFT worlsheet scattering theory and of integrable boundaries that manifest themselves as Dp-branes (p+1-dimensional Dirichlet submanifolds) which are a necessary part of the superstring theory. The presence of these objects breaks some of the underlying symmetries and leads to boundary scattering theory governed by coideal subalgebras of the bulk symmetry. Here the boundary scattering theory for D3-, D5- and D7-branes is considered in detail, and the underlying boundary Yangian symmetries are revealed.
The AdS/CFT worldsheet scattering theory is shown to be closely related to that of the deformed Hubbard chain. This similarity allows us to apply the quantum deformed approach to the boundary scattering theory. Such treatment of the system leads to quantum affine symmetries that manifest themselves in a very elegant and compact form. In such a way the symmetries of distinct boundaries that previously seemed to be unrelated to each other emerge in a uniform and coherent form.
The quantum deformed approach also helps us to better understand the phenomena of the so-called secret symmetry. It is called secret due to its peculiar feature of appearing as a level-one generator of the Yangian of the system. However it does not have a Lie algebra (level-zero) analogue. This symmetry is shown to have origins in the quantum deformed model, where it manifest itselfs as two, level-one and level-minus-one, generators of the corresponding quantum affine algebra.
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影响因子：
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影响因子：
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