标题： 一阶函数在AdS/dCFT中：MPS和扭曲杨代数 显示英文标题

标题： One-point functions in AdS/dCFT: MPS and twisted Yangian

摘要： 我专注于D5-D3探测膜设置中SO(6)子空间中的标量单点函数。 从积分性的一般介绍开始，我探讨了坐标Bethe假设和代数Bethe假设，以及可能的推广。 然后简要回顾如何在$N = 4$超杨-米尔斯理论中使用Bethe假设，然后将这种过程应用于D5-D3系统。 该系统的对偶场论对应于$N = 4$超杨-米尔斯理论的一个缺陷版本，其中某些标量的单点函数是非零的。 单点函数的计算被映射到矩阵乘积态和Bethe态之间的重叠。 发现矩阵乘积态是扭曲边界Yang-Baxter方程的解，等价于扩展扭曲Yangian的表示。 通过装饰过程或coproduct性质，我们可以将标量矩阵乘积态与更高维度的矩阵乘积态联系起来。 我们使用分支规则来找到与一些需要固定的详细参数的联系。 这种方法不仅可以用于探测膜系统中单点函数的计算，还可以为非平衡系统提供一些启示。 显示英文摘要

摘要： I focus on the scalar one-point functions in SO(6) sector of D5-D3 probe-brane set-up. Start with a general introduction of integrability, I explore both coordinate Bethe ansatz and algebraic Bethe ansatz, with possible generalization. I then shortly review how to use the Bethe ansatz in $N = 4$ super Yang-Mills theory, and then apply such procedure to the D5-D3 system. The dual field theory of such system corresponds to a defected version of $N = 4$ super Yang-Mills theory, where the one-point functions of certain scalars are non-zero. The calculation of one-point functions is mapped to the overlap between matrix product states and Bethe states. The matrix product states are found to be solutions of the twisted Boundary Yang-Baxter equation, and equivalently the representations of extended twisted Yangian. By dressing procedure or coproduct property, we can connect the scalar matrix product state and higher dimension matrix product states. We have used the branching rules to find the connection with some detailed parameters needed to be fixed. Such method can not only be used for calculations of one-point functions in probe-branes system, but also shed some light on non-equilibrium system.