论文标题
非几何t偶对作为具有连接的较高的群体捆
Non-Geometric T-Duality as Higher Groupoid Bundles with Connections
论文作者
论文摘要
我们将一般几何背景和非几何背景之间的T偶二维描述为具有连接的较高的群体束。我们的描述扩展了Nikolaus和Waldorf先前的观察结果，即可以用较高的几何形状来描述几何和半几何T二维的拓扑方面。我们以两种方式扩展了他们的构造。首先，我们将较高的几何形状赋予了调整后的连接，这使我们可以讨论T-background的度量标准和Kalb-Ramond场的明确公式。其次，我们将主要的2捆绑包扩展到增强的2组捆绑包，该束可容纳沿着多个方向的T偶尔以及$ Q $ - 和$ r $ $ $ - $ $ -FLUXES产生的标量字段。我们的描述显然是在完整的T-二维组$ \ mathsf {go}（n，n; n; \ mathbb {z}）$下的协变量，并且具有有趣的物理和数学含义。
We describe T-duality between general geometric and non-geometric backgrounds as higher groupoid bundles with connections. Our description extends the previous observation by Nikolaus and Waldorf that the topological aspects of geometric and half-geometric T-dualities can be described in terms of higher geometry. We extend their construction in two ways. First, we endow the higher geometries with adjusted connections, which allow us to discuss explicit formulas for the metric and the Kalb-Ramond field of a T-background. Second, we extend the principal 2-bundles to augmented 2-groupoid bundles, which accommodate the scalar fields arising in T-duality along several directions as well as $Q$- and $R$-fluxes. Our description is manifestly covariant under the full T-duality group $\mathsf{GO}(n,n;\mathbb{Z})$, and it has interesting physical and mathematical implications.
