非阿贝尔 T 对偶下的 $AdS_2 \times H^2 \times H^2$ 中的 D 膜
D-branes in $AdS_2 \times H^2 \times H^2$ under the non-Abelian T-duality
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中文总结 AI 辅助
研究在 $AdS_2 \times H^2 \times H^2$ 背景下通过非阿贝尔 T 对偶构建非阿贝尔对偶对，利用李群参数化构建原始模型，研究对偶时空行为及胶合矩阵情况，发现对相连膜的对称对偶作用。
中文摘要 AI 辅助
我们通过应用非阿贝尔 T 对偶（这里是半阿贝尔双上的泊松 - 李 T 对偶）为 $AdS_2 \times H^2 \times H^2$ 背景构建一个非阿贝尔对偶对。利用六维李群 ${A}_2 \otimes {A}_2 \otimes A_2$ 的特定参数化构建了不含 B 场时包含 $AdS_2 \times H^2 \times H^2$ 度规的原始 $\sigma$ 模型。结果表明，通过泊松 - 李 T 对偶构建的对偶背景由一个 B 场和一个包含物理奇点的度规支持。通过研究对偶时空在小 $(r, y, u)$ 坐标下的行为，表明零场强和非平凡伸缩子场的对偶度规构成了一圈 $\beta$ 函数方程消失的解。此外，在大 $(r, y, u)$ 时，表明 $AdS_2 \times H^2 \times H^2$ 解在非阿贝尔 T 对偶下保持不变。最后，利用从泊松 - 李 T 对偶的规范变换描述获得的对偶映射来确定局部定义 D 膜性质的胶合矩阵，我们找到了 $AdS_2 \times H^2 \times H^2$ $\sigma$ 模型及其对偶对的七种不同胶合矩阵情况。这样，在对偶链中发现了对相连膜的对称对偶作用。
英文摘要
We proceed to construct a non-Abelian dual pair for the $AdS_2 \times H^2 \times H^2$ background by applying the non-Abelian T-duality (here as Poisson-Lie T-duality on a semi-Abelian double). By using a certain parameterization of the $6$-dimensional Lie group ${A}_2 \otimes {A}_2 \otimes A_2$ we construct the original $σ$-model including the $AdS_2 \times H^2 \times H^2$ metric in the absence of $B$-field. It is shown that the dual background constructed by means of the Poisson-Lie T-duality is supported by a $B$-field and a metric whose contains a physical singularity. By studying the behavior of the dual spacetime at small $(r , y, u)$ coordinates, we show that the dual metric with a zero field strength and a non-trivial dilaton field make up a solution for the vanishing of the one-loop beta-function equations. Furthermore, at large $(r , y, u)$, it is shown that the $AdS_2 \times H^2 \times H^2$ solution is preserved under the non-Abelian T-duality. Finally, using the duality map obtained from the canonical transformation description of the Poisson-Lie T-duality for the gluing matrix which locally defines the properties of the D-brane, we find seven different cases of the gluing matrices for the $AdS_2 \times H^2 \times H^2$ $σ$-model and its dual pair. In this way, it is found a symmetric duality action on the branes linking together in a duality chain.
