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arXiv 2004.12858hep-thmath-phmath.MP
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基于流代数变形的WZW模型的Poisson-Lie T-对偶

Poisson-Lie T-Duality of WZW Model via Current Algebra Deformation

Francesco Bascone, Franco Pezzella, Patrizia Vitale

备注：
Final amended version. References added. 50 pages
发表信息：
JHEP 09 (2020) 060
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摘要：

研究了以$SU(2)$的群流形为目标空间的Wess-Zumino-Witten（WZW）模型的Poisson-Lie T-对偶.整个构造依赖于模型的仿射流代数的变形，半直和$\mathfrak{su}(2)(\mathbb{R}) \, \dot{\oplus} \, \mathfrak{a}$，完全半单卡茨-穆迪代数$\mathfrak{sl}(2,\mathbb{C})(\mathbb{R})$。以$SL(2,\mathbb{C})$为目标相空间，得到了一类双参数模型族，使得Poisson-Lie T-对偶在相空间中实现为$O(3,3)$的旋转.对偶族共享相同的相空间，但其位形空间是$SB(2,\mathbb{C})$，即群$SU(2)$的泊松-李对偶。在$SL(2,\mathbb{C})$上定义了一个双自由度的父作用，并给出了它的Hamilton描述.

英文摘要：

Poisson-Lie T-duality of the Wess-Zumino-Witten (WZW) model having the group manifold of $SU(2)$ as target space is investigated. The whole construction relies on the deformation of the affine current algebra of the model, the semi-direct sum $\mathfrak{su}(2)(\mathbb{R}) \, \dot{\oplus} \, \mathfrak{a}$, to the fully semisimple Kac-Moody algebra $\mathfrak{sl}(2,\mathbb{C})(\mathbb{R})$. A two-parameter family of models with $SL(2,\mathbb{C})$ as target phase space is obtained so that Poisson-Lie T-duality is realised as an $O(3,3)$ rotation in the phase space. The dual family shares the same phase space but its configuration space is $SB(2,\mathbb{C})$, the Poisson-Lie dual of the group $SU(2)$. A parent action with doubled degrees of freedom on $SL(2,\mathbb{C})$ is defined, together with its Hamiltonian description.

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