Discrete Symmetries Underlying Some Continuous Ones: Two Examples From Gravity And Particle Physics

(2+1)维引力与Chern-Simons理论中的量子双和$\kappa$-庞加莱对称性

Quantum double and $κ$-Poincaré symmetries in (2+1)-gravity and Chern-Simons theory

该研究综述量子双和κ-庞加莱对称性在(2+1)维引力与陈-西蒙斯理论中的作用，明确二者的相容条件，指出类时形变κ-庞加莱对称性仅在德西特情形下关联陈-西蒙斯理论，且该理论与(2+1)维引力物理不等价。

Symmetries of spacetime and their relation to initial value problems

We consider covariant metric theories of coupled gravity-matter systems satisfying the following two conditions: First, it is assumed that, by a hyperbolic reduction process, a system of first order symmetric hyperbolic partial differential equations can be deduced from the matter field equations. Second, gravity is supposed to be coupled to the matter fields by requiring that the Ricci tensor is a smooth function of the basic matter field variables and the metric. It is shown then that the ``time'' evolution of these type of gravity-matter systems preserves the symmetries of initial data spec…

Projective symmetries and induced electromagnetism in metric-affine gravity

We present a framework in which the projective symmetry of the Einstein-Hilbert action in metric-affine gravity is used to induce an effective coupling between the Dirac lagrangian and the Maxwell field. The effective $U(1)$ gauge potential arises as the trace of the non-metricity tensor $Q_{μa}{}^a$ and couples in the appropriate way to the Dirac fields to in order to allow for local phase shifts. On shell, the obtained theory is equivalent to Einstein-Cartan-Maxwell theory in presence of Dirac spinors.

Nonholonomic Deformations of Disk Solutions and Algebroid Symmetries in Einstein and Extra Dimension Gravity

In this article we consider nonholonomic deformations of disk solutions in general relativity to generic off-diagonal metrics defining knew classes of exact solutions in 4D and 5D gravity. These solutions possess Lie algebroid symmetries and local anisotropy and define certain generalizations of manifolds with Killing and/ or Lie algebra symmetries. For Lie algebroids, there are structures functions depending on variables on a base submanifold and it is possible to work with singular structures defined by the 'anchor' map. This results in a number of new physical implications comparing with th…

角点方案下的量子引力

Cornering Quantum Gravity

本文围绕引力的对称性展开，介绍协变相空间、诺特定理、渐近对称性及BMS群，阐述corner proposal等最新进展，探讨其对量子引力的意义。

规范PDE方法中引力的渐近对称性

Asymptotic symmetries of gravity in the gauge PDE approach

本文提出了基于规范PDE的框架研究带边流形上的局部规范理论与渐近对称性，将其应用于渐近平坦引力，通过导出边界规范PDE的极小模型得到共形Carollian结构并导出传统BMS代数。

BV-equivalence between triadic gravity and BF theory in three dimensions

The triadic description of General Relativity in three dimensions is known to be a BF theory. Diffeomorphisms, as symmetries, are easily re- covered on shell from the symmetries of BF theory. This note describes an explicit off-shell BV symplectomorphism between the BV versions of the two theories, each endowed with their natural symmetries.

Three-dimensional gravity and Drinfel'd doubles: spacetimes and symmetries from quantum deformations

We show how the constant curvature spacetimes of 3d gravity and the associated symmetry algebras can be derived from a single quantum deformation of the 3d Lorentz algebra sl(2,R). We investigate the classical Drinfel'd double of a "hybrid" deformation of sl(2,R) that depends on two parameters (η,z). With an appropriate choice of basis and real structure, this Drinfel'd double agrees with the 3d anti-de Sitter algebra. The deformation parameter ηis related to the cosmological constant, while z is identified with the inverse of the speed of light and defines the signature of the metric. We gene…

含体标量场的膜世界引力中宇宙学场方程的Lie对称性

Lie symmetries for the cosmological field equations in brane-world gravity with bulk scalar field

本研究在含非零质量体标量场的五维膜世界宇宙学框架下，通过Lie对称条件分析引力场方程的群分类，发现仅指数势存在Lie对称性，并利用Lie不变量构造相似变换得到了系统的精确解。

The gauge symmetries of f(R) gravity with torsion in the Cartan formalism

First-order general relativity in $n$ dimensions ($n \geq 3$) has an internal gauge symmetry that is the higher-dimensional generalization of three-dimensional local translations. We report the extension of this symmetry for $n$-dimensional f(R) gravity with torsion in the Cartan formalism. The new symmetry arises from the direct application of the converse of Noether's second theorem to the action principle of f(R) gravity with torsion. We show that infinitesimal diffeomorphisms can be written as a linear combination of the new internal gauge symmetry, local Lorentz transformations, and terms…

来自全纯圆盘的引力与天球 $Lw_{1+\infty}$ 对称性

Gravity from holomorphic discs and celestial $Lw_{1+\infty}$ symmetries

该研究在分裂号差下用实扭量空间的齐次生成函数编码渐近平坦自对偶引力数据，给出天球$Lw_{1+\infty}$对称性的最优表述，并将非自对偶引力振幅表述为扭量空间全纯圆盘理论，还讨论了相关延伸问题。

Chern-Simons、Yang-Mills 和 Einstein 引力的中心对称性的对称 TFT 三明治构造

Sandwich Construction of Symmetry TFTs for the Centre Symmetries of Chern-Simons, Yang-Mills, and Einstein Gravity

利用 Pulmann-Ševera-Valach 的三明治构造构建对称拓扑场论 (SymTFTs)，以显化 Chern-Simons 理论、Yang-Mills 理论以及 MacDowell-Mansouri 形式中广义相对论的中心对称性。

Carroll 膨胀引力离散 BF 形式中的和乐与边界对称性

Holonomies and Boundary Symmetries in the Discrete BF Formulation of Carroll Dilaton Gravity

基于 BF 型规范结构，利用格点上的和乐变量构建二维 Carroll 膨胀引力的离散实现，通过边界条件导出渐近对称性，得到仿射 Carroll 代数及其共形约化，为离散 Jackiw-Teitelboim 引力的超相对论对应。