Homogeneous Yang–Baxter deformations as non-abelian duals of the AdS5 σ-model
Homogeneous Yang–Baxter deformations as non-abelian duals of the AdS5 σ-model
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DOI：
10.1088/1751-8113/49/49/494001
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发表时间：
2016-09
期刊：
影响因子：
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通讯作者：
B. Hoare;A. Tseytlin
中科院分区：
文献类型：
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作者：
B. Hoare;A. Tseytlin
我们提出了由求解齐次（经典）Yang-Baxter方程的r-矩阵参数化的对称空间σ-模型的Yang-Baxter变形等价于未变形模型关于由r-矩阵结构确定的子群的非交换对偶.我们在AdS 5 σ模型的大量例子中明确地证明了这一点。对于完整的AdS 5 × S 5超陪集模型也是如此，通过T对偶和非线性坐标重定义的组合，提供了一个解释，并推广了最近几个将基于非交换r矩阵的齐次杨-巴克斯特变形与未变形的AdS 5 × S 5模型联系起来的观察结果。这也包括基于交换r-矩阵的变形的特殊情况，其对应于TsT变换：它们等价于原始模型关于交换子代数的中心扩展的非交换矩阵。
We propose that the Yang–Baxter deformation of the symmetric space σ-model parameterized by an r-matrix solving the homogeneous (classical) Yang–Baxter equation is equivalent to the non-abelian dual of the undeformed model with respect to a subgroup determined by the structure of the r-matrix. We explicitly demonstrate this on numerous examples in the case of the AdS 5 σ-model. The same should also be true for the full AdS 5 × S 5 supercoset model, providing an explanation for and generalizing several recent observations relating homogeneous Yang–Baxter deformations based on non-abelian r-matrices to the undeformed AdS 5 × S 5 model by a combination of T-dualities and nonlinear coordinate redefinitions. This also includes the special case of deformations based on abelian r-matrices, which correspond to TsT transformations: they are equivalent to non-abelian duals of the original model with respect to a central extension of abelian subalgebras.