发表机构
Kyung Hee University; Scuola Normale Superiore and INFN（庆熙大学; 比萨高等师范学院和意大利国家核物理研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究三维平直全息中Carroll-Weyl对称性的实现，证明爱因斯坦引力仅支持体积调制变换，而共形引力通过体胀子实现两种变换，并推导出中心扩展代数及边界反常预言。
AI 中文摘要
零边界的退化几何允许一个扩大的局部共形自由度：在二维中，Carrollian余框架允许两个独立的Weyl重标度，一个调制边界体积形式，另一个保持它。我们研究这两种变换是否都能在三维平直全息中实现为带荷渐近对称性。我们证明爱因斯坦引力正则地实现体积调制Carroll-Weyl变换以及局部Carroll提升，但不允许体积保持重标度作为额外的独立渐近对称性。我们将这一阻碍追溯到零无穷远的共形完备化以及庞加莱代数中缺乏两个独立的交换半单生成元。共形引力通过体胀子克服了这一阻碍，提供了缺失的代数方向。我们构造了一个渐近平坦的共形引力相空间，在其中两种Carroll-Weyl变换和局部Carroll提升都允许有限、可积且通常非零的正则荷，并推导出它们的中心扩展代数。最后，我们表明这些中心扩展通过辛下降产生于边界反常，从而为平直全息中的Carroll-Weyl反常提供了引力预言。
英文摘要
The degenerate geometry of a null boundary admits an enlarged local conformal freedom: in two dimensions, a Carrollian coframe allows two independent Weyl rescalings, one modulating and the other preserving the boundary volume form. We investigate whether both transformations can be realized as charged asymptotic symmetries in three-dimensional flat holography. We show that Einstein gravity canonically realizes the volume-modulating Carroll-Weyl transformation, together with local Carroll boosts, but does not admit the volume-preserving rescaling as an additional independent asymptotic symmetry. We trace this obstruction both back to the conformal completion of null infinity and to the absence of two independent commuting semisimple generators in the Poincaré algebra. Conformal gravity overcomes this obstruction through bulk dilatations, which supply the missing algebraic direction. We construct an asymptotically flat phase space of conformal gravity in which both types of Carroll-Weyl transformations and local Carroll boosts admit finite, integrable, and generically nonvanishing canonical charges, and derive their centrally extended algebra. Finally, we show that these central extensions arise from boundary anomalies through symplectic descent, yielding a gravitational prediction for Carroll-Weyl anomalies in flat holography.
Comments44 pages
