标题： 非阿贝尔目标空间对偶的Thurston几何 显示英文标题

标题： Non-Abelian target space duals of Thurston geometries

摘要： 在本研究中，我们从Poisson-Lie（PL）T对偶性的角度来探讨Thurston几何。首先，我们找到所有生成在三维目标流形上自由且传递作用的等距群的Killing矢量的子代数，在这些流形上定义了Thurston度规。研究表明，三维李子代数同构于Bianchi型代数。我们将度规的等距子群作为Drinfeld双的第一子群。为了研究非阿贝尔T对偶性，第二子群必须选择为阿贝尔的。因此，通过PL T对偶性方法，在没有$B$场的情况下找到了这些几何的非阿贝尔目标空间对偶。我们还讨论了所考虑的T对偶$\sigma$模型的共形不变性条件。 显示英文摘要

摘要： In this study, we proceed to investigate the Thurston geometries from the point of view of their Poisson-Lie (PL) T-dualizability. First of all, we find all subalgebras of Killing vectors that generate group of isometries acting freely and transitively on the three-dimensional target manifolds, where the Thurston metrics are defined. It is shown that three-dimensional Lie subalgebras are isomorphic to the Bianchi type algebras. We take the isometry subgroup of the metric as the first subgroup of Drinfeld double. In order to investigate the non-Abelian T-duality, the second subgroup must be chosen to be Abelian. Accordingly, the non-Abelian target space duals of these geometries are found via PL T-duality approach in the absence of $B$-field. We also comment on the conformal invariance conditions of the T-dual $\sigma$-models under consideration.