Weyl vs. Conformal
英文摘要:
In this note we show that given a conformally invariant theory in flat space-time, it is not always possible to couple it to gravity in a Weyl invariant way.
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Georgios K. Karananas, Alexander Monin
In this note we show that given a conformally invariant theory in flat space-time, it is not always possible to couple it to gravity in a Weyl invariant way.
机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。
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A conformally invariant differential operator on Weyl tensor densities
本文给出了共形四维流形上四阶共形不变微分算子的张量公式。该算子适用于某个共形权的代数外尔张量密度,并在另一个权的代数外尔张量密度中取其值。对于定向流形,这个算子颠倒了对偶性:例如在黎曼的情况下,它将自对偶张量取为反自对偶张量,反之亦然。我们还研究的地方,这个运营商在已知的结果共形不变的运营商的分类占据,我们研究了一些相关的运营商。
Does Superstring Theory Have a Conformally Invariant Limit?
这个演讲描述了一个建议,由于赫尔,共形不变的极限超弦理论在六个维度。
Celestial diamonds encode the structure of global conformal multiplets in 2D celestial CFT and offer a natural language for describing the conformally soft sector. The operators appearing at their left and right corners give rise to conformally soft factorization theorems, the bottom corners correspond to conserved charges, and the top corners to conformal dressings. We show that conformally soft charges can be expressed in terms of light ray integrals that select modes of the appropriate conformal weights. They reside at the bottom corners of memory diamonds, and ascend to generalized current…
A new class of conformal field theories is presented, where the background gravitational field is conformally flat. Conformally flat (CF) spacetimes enjoy conformal properties quite similar to the ones of flat spacetime. The conformal isometry group is of maximal rank and the conformal Killing vectors in conformally flat coordinates are {\em exactly} the same as the ones of flat spacetime. In this work, a new concept of distance is introduced, the {\em conformal distance}, which transforms covariantly under all conformal isometries of the CF space. It is shown that precisely for CF spacetimes,…
A new method for the construction of conformally invariant equations in an arbitrary four dimensional (pseudo-) Riemannian space is presented. This method uses the Weyl geometry as a tool and exploits the natural conformal invariance we can build in the framework of this geometry. Indeed, working in a Weyl space, using the Weyl covariant derivative and the intrinsic Weylian geometrical tensors, all conformally homogeneous operators will be conformally invariant, as will the equations they determine. A Weyl space is defined by two independent objects: the metric tensor $g_{μν}$ and the Weyl vec…
Spontaneous breaking of conformal invariance in theories of conformally coupled matter and Weyl gravity
研究了在共形不变相互作用下具有物质自由度的Weyl共形引力理论。具体地说,我们考虑了一个三重态的标量场和SO(3)非阿贝尔规范场,即Georgi-Schmidhow模型与Weyl引力共形耦合.我们发现,运动方程承认解决方案自发打破共形对称性和规范对称性,提供了一个机制,提供了一个规模的理论。真空解对应反德西特时空,而局域孤子解对应渐近反德西特时空中的磁单极子。由此产生的有效作用量产生了爱因斯坦引力和剩余U(1)规范理论。这一机制加强了共形不变的物质引力理论,这已经显示出有希望的迹象,在银河系旋转曲线失踪的问题考虑的理由。
Non-conformally flat bulk spacetime and the 3-brane world
我们证明了对于非共形平坦的体时空,在3-膜上不存在零质量引力子的束缚模。因此,对于不同于共形平坦反德西特空间的体时空,膜世界模型是不稳定的。
Volume and Area Renormalizations for Conformally Compact Einstein Metrics
本文描述了最近通过Anti-de Sitter/Conformal域论对应发现的共形紧Einstein流形及其极小子流形的几何不变量和共形反常.
We present a simple, systematic and practical method to construct conformally invariant equations in arbitrary Riemann spaces. This method that we call "Weyl-to-Riemann" is based on two features of Weyl geometry. i) A Weyl space is defined by the metric tensor and the Weyl vector $W$, it becomes equivalent to a Riemann space when $W$ is gradient. ii) Any homogeneous differential equation written in a Weyl space by means of the Weyl connection is conformally invariant. The Weyl-to-Riemann method selects those equations whose conformal invariance is preserved when reducing to a Riemann space. Ap…
We show that the averaged null energy condition can be violated by a conformally coupled scalar field in a conformally flat spacetime in 3+1 dimensions. The violation is dependent on the quantum state and can be made as large as desired. It does not arise from the presence of anomalies, although anomalous violations are also possible. Since all geodesics in conformally flat spacetimes are achronal, the achronal averaged null energy condition is likewise violated.
We study Weyl symmetry (local conformal symmetry) in unimodular gravity. It is shown that the Noether currents for both Weyl symmetry and global scale symmetry, identically vanish as in the conformally invariant scalar-tensor gravity. We clearly explain why in the class of conformally invariant gravitational theories, the Noether currents vanish by starting with the conformally invariant scalar-tensor gravity. Moreover, we comment on both classical and quantum-mechanical equivalences among Einstein's general relativity, the conformally invariant scalar-tensor gravity and the Weyl-transverse (W…
It is showed by a conformal rescaling that the inflationary background can be dual to a slowly expanding background, which is almost Minkowski and described by a conformal field theory conformally coupled to gravity. It is proved that the primordial curvature perturbation and tensor perturbation generated during these two conformally equivalent backgrounds are completely equal, and the scale invariance of perturbations is determined by the conformal invariance of field theory in slowly expanding background. In dual slowly expanding scenario, the primordial universe is asymptotical to a static …
The C-metric solution of conformal gravity with a conformally coupled scalar field is presented. The solution belongs to the class of Petrov type D spacetimes and is conformal to the standard AdS C-metric appeared in vacuum Einstein gravity. For all parameter ranges, we identify some of the physically interesting static regions and the corresponding coordinate ranges. The solution may contain a black hole event horizon, an acceleration horizon, either of which may be cut by the conformal infinity or be hidden behind the conformal infinity. Since the model is conformally invariant, we also disc…
Boundary regularity of conformally compact Einstein metrics
我们证明了C^2共形紧的黎曼爱因斯坦度量在3维和所有偶数维上都具有光滑的共形紧化,并且在大于3的奇数维上是多齐性的。
The gravitational energy-momentum pseudo-tensor of conformally invariant theories of gravity
本文构造了高达四阶共形不变引力理论的引力能量-动量赝张量,通过线性化并求宏观区域平均值,计算了三种主要共形不变引力理论中平面引力波携带的能量与动量。
The conformally invariant Laplace-Beltrami operator and factor ordering
在量子力学中,单个粒子的动能项通常写成拉普拉斯-贝尔特拉米算符的形式。该算子是经典动能的因子序。我们调查其他相对简单的因子排序,并表明,{ \it唯一}的其他解决方案的共形平坦的度量是共形不变的Laplace-Beltrami算子。对于非共形平坦度量,这种类型的因子排序失败,只有一个术语,给出共形不变的拉普拉斯-贝尔特拉米算子。
We build the general conformally invariant linear wave operator for a free, symmetric, second-rank tensor field in a d-dimensional ($d\geqslant 2$) metric manifold, and explicit the special case of maximally symmetric spaces. Under the assumptions made, this conformally invariant wave operator is unique. The corresponding conformally invariant wave equation can be obtained from a Lagrangian which is explicitly given. We discuss how our result compares to previous works, in particular we hope to clarify the situation between conflicting results.
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