Universal description of viscoelasticity with foliation preserving diffeomorphisms

Universal description of viscoelasticity with foliation preserving diffeomorphisms

We review our recent proposal for a universal description of generic single-component viscoelastic systems with a single relaxation time. Foliation preserving diffeomorphisms are introduced as an underlying symmetry which naturally interpolates between the two extreme characters of elasticity and fluidity. The symmetry is found to be powerful enough to determine the dynamics in the first order of strains.

时间切片中的 Wick 旋转、可容许复度规与改变叶状结构的微分同胚

Wick rotation in the lapse, admissible complex metrics, and foliation changing diffeomorphisms

本文提出在时间切片中进行 Wick 旋转以连接黎曼与洛伦兹度规，证明其复度规的可容许性及 Hessian 谱性质，并分析了与 Feynman $iε$ 规定和时间 Wick 旋转的差异。

On geodesics in space-times with a foliation structure: A spectral geometry approach

Motivated by the Horava-Lifshitz type theories, we study the physical motion of matter coupled to a foliated geometry in non-diffeomorphism invariant way. We use the concept of a spectral action as a guiding principle in writing down the matter action. Based on the deformed Dirac operator compatible with the reduced symmetry - foliation preserving diffeomorphisms, this approach provides a natural generalization of the minimal coupling. Focusing on the IR version of the Dirac operator, we derive the physical motion of a test particle and discuss in what sense it still can be considered as a geo…

Phenomenologically viable gravitational theory based on a preferred foliation without extra modes

We present a gravitational field theory that implements Horava's proposal of foliation-preserving-diffeomorphisms symmetry and higher spatial curvature directly in the canonical formalism. Due to the higher spatial derivative the theory is potentially renormalizable. Since this gauge symmetry is natural in the canonical formalism, we do not require a Lagrangian of second-order in time derivatives to begin with. We define the nonzero part of the Hamiltonian and the constraints motivated by the kinetic-conformal version of the nonprojectable Horava theory. The resulting theory is an extension of…

非测地叶状结构上的时空对称性破缺与一种新物质形态

Space-time symmetry breaking on non-geodesic leaves and a new form of matter

本文研究叶状结构破坏微分同胚不变性后遗留的哈密顿量与动量如何表现为一种无空间应力但具有能量和动量流的新型物质形式，并以Rindler时空和Schwarzschild参考系为例加以说明。

Holographic Renormalization of Foliation Preserving Gravity and Trace Anomaly

From the holographic renormalizationg group viewpoint, while the scale transformation plays a primary role in the duality by providing the extra dimension, the special conformal transformation seems to only play a secondary role. We, however, claim that the space-time diffeomorphism is crucially related to the latter. For its demonstration, we study the holographic renormalization group flow of a foliation preserving diffeomophic theory of gravity (a.k.a. space-time flipped Horava gravity). We find that the dual field theory, if any, is only scale invariant but not conformal invariant. In part…