AI 中文总结
本文从全息原理直接得到三维渐近平直时空对偶的二维 Carrollian 共形场论的中心荷，构造其全息准局域应力张量，推导边界 BMS Schwarzian 模式的作用量，并验证相关守恒定律。
AI 中文摘要
我们研究三维渐近平直时空的全息原理，其体引力动力学被推测对偶于二维 Carrollian（等价于 BMS）共形场论。这类理论被认为是相对论性二维共形场论的超相对论（$c\rightarrow0$）收缩产物，在此收缩下，Virasoro 代数变为共形 Carrollian 代数，Brown-Henneaux 中心荷变为 $c_L=0$、$c_M=\frac{3}{G}$。本文我们直接从全息原理得到这些中心荷：首先构造携带 Bondi 质量和角动量的渐近平直时空的全息准局域应力张量，在 BMS$_3$ 变换下，该应力张量获得名为“BMS Schwarzian”的非齐次项，从中提取中心荷可精确复现代数结果；随后得到边界 BMS Schwarzian 模式的作用量；最后证明全息应力张量关联函数满足预期的 Ward 恒等式，而应力张量守恒服从通量平衡定律。
英文摘要
We study holography for three-dimensional asymptotically flat spacetimes in which the bulk gravitational dynamics is conjectured to be dual to a two-dimensional Carrollian (equivalently BMS) conformal field theory. Such theories are known to arise as ultrarelativistic ($c\rightarrow0$) contractions of relativistic 2d conformal field theories. Under this contraction, the Virasoro algebra becomes the conformal Carrollian algebra and the Brown-Henneaux central charges become $c_L=0$, $c_M=\frac{3}{G}$. In this article, we recover these central charges directly from holography. We first construct the holographic quasilocal stress tensor for asymptotically flat spacetimes carrying Bondi mass and angular momentum. Under BMS$_3$ transformations, the stress tensor acquires an inhomogeneous term, the ``BMS Schwarzian", and extracting the central charges from it reproduces the algebraic result exactly. We then obtain the action for the boundary BMS Schwarzian modes. Finally, we show that the holographic stress-tensor correlators satisfy the expected Ward identity, while stress-tensor conservation obeys flux-balance laws.
