scholarly journals THE LOWEST MODES AROUND GAUSSIAN SOLUTIONS OF TENSOR MODELS AND THE GENERAL RELATIVITY

2008 ◽  
Vol 23 (24) ◽  
pp. 3863-3890 ◽  
Author(s):  
NAOKI SASAKURA
Keyword(s):  
General Relativity ◽  
Two Dimensions ◽  
Tensor Model ◽  
Momentum Dependence ◽  
Two Dimensional ◽  
Renormalization Procedure ◽  
Metric Tensor ◽  
Tensor Models ◽  
General Coordinate Transformation ◽  
Metric Fluctuations

In the paper arXiv:0706.1618[hep-th], the number distribution of the low-lying spectra around Gaussian solutions representing various dimensional fuzzy tori of a tensor model was numerically shown to be in accordance with the general relativity on tori. In this paper, I perform more detailed numerical analysis of the properties of the modes for two-dimensional fuzzy tori, and obtain conclusive evidences for the agreement. Under a proposed correspondence between the rank-3 tensor in tensor models and the metric tensor in the general relativity, conclusive agreement is obtained between the profiles of the low-lying modes in a tensor model and the metric modes transverse to the general coordinate transformation. Moreover, the low-lying modes are shown to be well on a massless trajectory with quartic momentum dependence in the tensor model. This is in agreement with that the lowest momentum dependence of metric fluctuations in the general relativity will come from the R2-term, since the R-term is topological in two dimensions. These evidences support the idea that the low-lying low-momentum dynamics around the Gaussian solutions of tensor models is described by the general relativity. I also propose a renormalization procedure for tensor models. A classical application of the procedure makes the patterns of the low-lying spectra drastically clearer, and suggests also the existence of massive trajectories.

scholarly journals THE FLUCTUATION SPECTRA AROUND A GAUSSIAN CLASSICAL SOLUTION OF A TENSOR MODEL AND THE GENERAL RELATIVITY

2008 ◽  
Vol 23 (05) ◽  
pp. 693-718 ◽  
Author(s):  
NAOKI SASAKURA
Keyword(s):  
General Relativity ◽  
Classical Solution ◽  
Flat Space ◽  
Effective Field ◽  
Tensor Model ◽  
Metric Tensor ◽  
Four Dimensions ◽  
Tensor Models ◽  
Momentum Spectra ◽  
General Coordinate Transformation

Tensor models can be interpreted as theory of dynamical fuzzy spaces. In this paper, I study numerically the fluctuation spectra around a Gaussian classical solution of a tensor model, which represents a fuzzy flat space in arbitrary dimensions. It is found that the momentum distribution of the low-lying low-momentum spectra is in agreement with that of the metric tensor modulo the general coordinate transformation in the general relativity at least in the dimensions studied numerically, i.e. one to four dimensions. This result suggests that the effective field theory around the solution is described in a similar manner as the general relativity.

scholarly journals A RENORMALIZATION PROCEDURE FOR TENSOR MODELS AND SCALAR-TENSOR THEORIES OF GRAVITY

2010 ◽  
Vol 25 (23) ◽  
pp. 4475-4492 ◽  
Author(s):  
NAOKI SASAKURA
Keyword(s):  
General Relativity ◽  
Models Of Quantum Gravity ◽  
Quantum Gravity ◽  
Matrix Models ◽  
Dynamical Variable ◽  
Renormalization Procedure ◽  
Emergent Phenomena ◽  
Tensor Models ◽  
Theories Of Gravity

Tensor models are more-index generalizations of the so-called matrix models, and provide models of quantum gravity with the idea that spaces and general relativity are emergent phenomena. In this paper, a renormalization procedure for the tensor models whose dynamical variable is a totally symmetric real three-tensor is discussed. It is proven that configurations with certain Gaussian forms are the attractors of the three-tensor under the renormalization procedure. Since these Gaussian configurations are parametrized by a scalar and a symmetric two-tensor, it is argued that, in general situations, the infrared dynamics of the tensor models should be described by scalar-tensor theories of gravity.

TENSOR MODEL FOR GRAVITY AND ORIENTABILITY OF MANIFOLD

1991 ◽  
Vol 06 (28) ◽  
pp. 2613-2623 ◽  
Author(s):  
NAOKI SASAKURA
Keyword(s):  
Quantum Gravity ◽  
Hermitian Matrix ◽  
Three Dimensional ◽  
Tensor Model ◽  
Two Dimensional ◽  
Tensor Models ◽  
Arbitrary Dimensions ◽  
Dynamical Triangulation ◽  
Hermitian Matrix Model ◽  
Special Case

We investigate the relation between rank-three tensor models and the dynamical triangulation model of three-dimensional quantum gravity, and discuss the orientability of the manifold and the corresponding tensor models. We generalize the orientable tensor models to arbitrary dimensions, which include the two-dimensional Hermitian matrix model as a special case.

scholarly journals CANONICAL TENSOR MODELS WITH LOCAL TIME

2012 ◽  
Vol 27 (05) ◽  
pp. 1250020 ◽  
Author(s):  
NAOKI SASAKURA
Keyword(s):  
Field Theory ◽  
General Relativity ◽  
Local Time ◽  
String Field Theory ◽  
Dynamical Variable ◽  
Tensor Model ◽  
Canonical Variables ◽  
Hamilton Formalism ◽  
Tensor Models ◽  
Constraint Algebra

It is an intriguing question how local time can be introduced in the emergent picture of space–time. In this paper, this problem is discussed in the context of tensor models. To consistently incorporate local time into tensor models, a rank-three tensor model with first class constraints in Hamilton formalism is presented. In the limit of usual continuous spaces, the algebra of constraints reproduces that of general relativity in Hamilton formalism. While the momentum constraints can be realized rather easily by the symmetry of the tensor models, the form of the Hamiltonian constraints is strongly limited by the condition of the closure of the whole constraint algebra. Thus the Hamiltonian constraints have been determined on the assumption that they are local and at most cubic in canonical variables. The form of the Hamiltonian constraints has similarity with the Hamiltonian in the c < 1 string field theory, but it seems impossible to realize such a constraint algebras in the framework of vector or matrix models. Instead these models are rather useful as matter theories coupled with the tensor model. In this sense, a three-index tensor is the minimum-rank dynamical variable necessary to describe gravity in terms of tensor models.

Urbanicity, City Delegations, and Two-Dimensional Liberalism

2018 ◽  
Author(s):  
Thomas K. Ogorzalek
Keyword(s):  
National Level ◽  
Two Dimensions ◽  
Political Order ◽  
Two Dimensional ◽  
Local Institutions ◽  
Horizontal Integration ◽  
National Politics ◽  
United Front ◽  
Strategies For Success

This theoretical chapter develops the argument that the conditions of cities—large, densely populated, heterogeneous communities—generate distinctive governance demands supporting (1) market interventions and (2) group pluralism. Together, these positions constitute the two dimensions of progressive liberalism. Because of the nature of federalism, such policies are often best pursued at higher levels of government, which means that cities must present a united front in support of city-friendly politics. Such unity is far from assured on the national level, however, because of deep divisions between and within cities that undermine cohesive representation. Strategies for success are enhanced by local institutions of horizontal integration developed to address the governance demands of urbanicity, the effects of which are felt both locally and nationally in the development of cohesive city delegations and a unified urban political order capable of contending with other interests and geographical constituencies in national politics.

scholarly journals Interface Roughening in Two Dimensions

2021 ◽  
Vol 182 (3) ◽  
Author(s):  
Gernot Münster ◽  
Manuel Cañizares Guerrero
Keyword(s):  
Field Theory ◽  
Monte Carlo ◽  
Capillary Wave ◽  
System Size ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Wave Approximation ◽  
Statistical Field ◽  
Statistical Field Theory ◽  
Interface Roughening

AbstractRoughening of interfaces implies the divergence of the interface width w with the system size L. For two-dimensional systems the divergence of $$w^2$$ w 2 is linear in L. In the framework of a detailed capillary wave approximation and of statistical field theory we derive an expression for the asymptotic behaviour of $$w^2$$ w 2 , which differs from results in the literature. It is confirmed by Monte Carlo simulations.

scholarly journals Is contact angle a cause or an effect? – A cautionary tale

2020 ◽  
Vol 146 ◽  
pp. 03004
Author(s):  
Douglas Ruth
Keyword(s):  
Contact Angle ◽  
Solid Surface ◽  
Contact Angles ◽  
Two Dimensions ◽  
Experimental Results ◽  
Flow In Porous Media ◽  
Two Dimensional ◽  
Wide Range ◽  
Fluid Drop ◽  
Surrounding Fluid

The most influential parameter on the behavior of two-component flow in porous media is “wettability”. When wettability is being characterized, the most frequently used parameter is the “contact angle”. When a fluid-drop is placed on a solid surface, in the presence of a second, surrounding fluid, the fluid-fluid surface contacts the solid-surface at an angle that is typically measured through the fluid-drop. If this angle is less than 90°, the fluid in the drop is said to “wet” the surface. If this angle is greater than 90°, the surrounding fluid is said to “wet” the surface. This definition is universally accepted and appears to be scientifically justifiable, at least for a static situation where the solid surface is horizontal. Recently, this concept has been extended to characterize wettability in non-static situations using high-resolution, two-dimensional digital images of multi-component systems. Using simple thought experiments and published experimental results, many of them decades old, it will be demonstrated that contact angles are not primary parameters – their values depend on many other parameters. Using these arguments, it will be demonstrated that contact angles are not the cause of wettability behavior but the effect of wettability behavior and other parameters. The result of this is that the contact angle cannot be used as a primary indicator of wettability except in very restricted situations. Furthermore, it will be demonstrated that even for the simple case of a capillary interface in a vertical tube, attempting to use simply a two-dimensional image to determine the contact angle can result in a wide range of measured values. This observation is consistent with some published experimental results. It follows that contact angles measured in two-dimensions cannot be trusted to provide accurate values and these values should not be used to characterize the wettability of the system.

scholarly journals Calderón problem for Maxwell's equations in two dimensions

2016 ◽  
Vol 24 (3) ◽  
Author(s):  
Oleg Y. Imanuvilov ◽  
Masahiro Yamamoto
Keyword(s):  
Maxwell’S Equations ◽  
Maxwell Equations ◽  
Maxwell's Equations ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Global Uniqueness ◽  
Calderón Problem ◽  
Dirichlet To Neumann Map

AbstractWe prove the global uniqueness in determination of the conductivity, the permeability and the permittivity of the two-dimensional Maxwell equations by the partial Dirichlet-to-Neumann map limited to an arbitrary subboundary.

Estimates of critical percolation probabilities for a set of two-dimensional lattices

1972 ◽  
Vol 71 (1) ◽  
pp. 97-106 ◽  
Author(s):  
D. G. Neal
Keyword(s):  
Monte Carlo ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Critical Percolation ◽  
Site Percolation

AbstractThis paper describes new detailed Monte Carlo investigations into bond and site percolation problems on the set of eleven regular and semi-regular (Archimedean) lattices in two dimensions.

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