We consider Einstein gravity on a patch of AdS$_3$ spacetime between two radii $r_1, r_2$. We compute surface charges and their algebra at an arbitrary radius $r$ such that it reduces to a given set of surface charges at $r_1, r_2$. The $r$-dependent charges become integrable upon addition of an appropriate boundary $Y$-term. We observe that soft excitations at each boundary are independent of those at the other boundary. We explicitly construct solution geometries which interpolate between these radii with specified surface charges. The interpolation is smooth provided that the mass and angular momentum measured at the two boundaries are equal.

中文翻译：

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AdS3 上的滑动表面电荷

我们在两个半径 $r_1, r_2$ 之间的一块 AdS$_3$ 时空上考虑爱因斯坦引力。我们计算任意半径 $r$ 处的表面电荷及其代数，使其减少到 $r_1, r_2$ 处的一组给定表面电荷。在添加适当的边界 $Y$ 项后，$r$ 相关费用变得可积分。我们观察到每个边界的软激发与另一个边界的软激发无关。我们明确地构建了解决方案几何图形，这些几何图形在具有指定表面电荷的这些半径之间进行插值。如果在两个边界处测量的质量和角动量相等，则插值是平滑的。