Carrollian 共形动力学与平直时空全息原理
Carrollian Conformal Dynamics and Flat-Space Holography
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中文总结 AI 辅助
本文提出度规-仿射 Carrollian 共形动力学框架，应用于渐近平直时空爱因斯坦引力，从边界内禀推导出 Bondi 演化方程，为平直时空全息中的辐射自由度提供几何实现。
中文摘要 AI 辅助
渐近平直时空的共形边界是类光的，因此携带的是 Carrollian 几何而非 Lorentzian 几何。这从根本上改变了对称性、变分原理与演化方程之间的关系：与 Lorentzian Levi-Civita 联络不同，与共形结构相容的无挠 Carrollian 联络包含真正的独立数据。我们发展了一种共形动力学的度规-仿射表述，通过超动量来追踪这些联络自由度。局域 Carroll 助推、旋转、Weyl 变换和微分同胚因此蕴含一组协变演化方程。我们将此框架应用于四维渐近平直时空中的爱因斯坦引力。Penrose 共形紧化将零无穷远识别为共形 Carrollian 流形；其相容联络中未确定的横向对称部分是渐近 Bondi 剪切。在固定 Bondi-van der Burg-Metzner-Sachs (BMS) 标架并将 Carrollian 动量和超动量与 Bondi 数据等同后，一般的 Carrollian 演化方程重现了质量和角动量方面的标准演化方程。该结果提供了引力演化方程的边界内禀推导，以及平直时空全息中辐射自由度的几何实现。本文是 2025 年 12 月 17-19 日在雅典国立卡波季斯特里安大学举行的“雅典理论物理研讨会：十周年”的会议录贡献。
英文摘要
The conformal boundary of asymptotically flat spacetime is null and therefore carries a Carrollian rather than Lorentzian geometry. This changes the relation between symmetry, variational principles and evolution equations in an essential way: unlike a Lorentzian Levi-Civita connection, a torsion-free Carrollian connection compatible with the conformal structure contains genuine independent data. We develop a metric-affine formulation of conformal dynamics that keeps track of these connection degrees of freedom through hypermomenta. Local Carroll boosts, rotations, Weyl transformations and diffeomorphisms then imply a set of covariant evolution equations. We apply this framework to Einstein gravity in four-dimensional asymptotically flat spacetimes. Penrose's conformal compactification identifies null infinity as a conformal Carrollian manifold; the undetermined transverse symmetric part of its compatible connection is the asymptotic Bondi shear. After fixing a Bondi-van der Burg-Metzner-Sachs (BMS) frame and identifying the Carrollian momenta and hypermomenta with the Bondi data, the general Carrollian evolution equations reproduce the standard evolution equations for the mass and angular-momentum aspects. The result provides a boundary-intrinsic derivation of the gravitational evolution equations and a geometric realization of radiative degrees of freedom in flat-space holography. This is a proceedings contribution to the "Athens Workshop in Theoretical Physics: 10th Anniversary", held at the National and Kapodistrian University of Athens on December 17-19 2025.
发表机构
- International School for Advanced Studies (SISSA)（高级研究国际学校）
- Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Trieste（意大利国家核物理研究所的里雅斯特分部）
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