论文标题
Courant支架作为Lie Bracket的T对偶不变延伸
Courant bracket as T-dual invariant extension of Lie bracket
论文作者
论文摘要
我们考虑封闭的骨弦的对称性，从一般坐标转换开始。他们的发电机将矢量成分$ξ^μ$作为其参数，其泊松支架代数产生其参数的谎言括号。我们将扩展该发电机，以使其在自t偶数上不变，即在同一相位空间中实现的t偶数性。新的发电机是$ 2D $ double Symmetry参数$λ$的函数，即矢量组件的直接总和$ξ^μ$和1型组件$λ_μ$。新发电机的泊松支架代数产生了库兰特支架，与一般坐标转换的代数产生的代数相同。从这个意义上讲，Courant支架是Lie支架的T二不变延伸。当将KALB-Ramond场引入模型时，构建了管理通用坐标和局部规格对称性的生成器。它不再是自t偶对齐，其代数产生了$ b $ twist的courant括号，而在其自t二偶描述中，相关的支架变成了$θ$ twist的courant courant支架。接下来，我们考虑取决于初始坐标的$ x^μ$和t偶坐标$ y__ $的T-偶数和对称参数。这些转换的发电机被定义为在双空间中的内部产品，其代数产生了C型支架。
We consider the symmetries of a closed bosonic string, starting with the general coordinate transformations. Their generator takes vector components $ξ^μ$ as its parameter and its Poisson bracket algebra gives rise to the Lie bracket of its parameters. We are going to extend this generator in order for it to be invariant upon self T-duality, i.e. T-duality realized in the same phase space. The new generator is a function of a $2D$ double symmetry parameter $Λ$, that is a direct sum of vector components $ξ^μ$, and 1-form components $λ_μ$. The Poisson bracket algebra of a new generator produces the Courant bracket in a same way that the algebra of the general coordinate transformations produces Lie bracket. In that sense, the Courant bracket is T-dual invariant extension of the Lie bracket. When the Kalb-Ramond field is introduced to the model, the generator governing both general coordinate and local gauge symmetries is constructed. It is no longer self T-dual and its algebra gives rise to the $B$-twisted Courant bracket, while in its self T-dual description, the relevant bracket becomes the $θ$-twisted Courant bracket. Next, we consider the T-duality and the symmetry parameters that depend on both the initial coordinates $x^μ$ and T-dual coordinates $y_μ$. The generator of these transformations is defined as an inner product in a double space and its algebra gives rise to the C-bracket.
