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 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 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.

scholarly journals Massive gravity from double copy

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Arshia Momeni ◽  
Justinas Rumbutis ◽  
Andrew J. Tolley
Keyword(s):  
Sigma Model ◽  
Massive Gravity ◽  
Effective Field ◽  
Effective Theory ◽  
Nonlinear Sigma Model ◽  
Limit Theory ◽  
Four Dimensions ◽  
Yang Mills ◽  
Massive Spin ◽  
Double Copy

Abstract We consider the double copy of massive Yang-Mills theory in four dimensions, whose decoupling limit is a nonlinear sigma model. The latter may be regarded as the leading terms in the low energy effective theory of a heavy Higgs model, in which the Higgs has been integrated out. The obtained double copy effective field theory contains a massive spin-2, massive spin-1 and a massive spin-0 field, and we construct explicitly its interacting Lagrangian up to fourth order in fields. We find that up to this order, the spin-2 self interactions match those of the dRGT massive gravity theory, and that all the interactions are consistent with a Λ3 = (m2MPl)1/3 cutoff. We construct explicitly the Λ3 decoupling limit of this theory and show that it is equivalent to a bi-Galileon extension of the standard Λ3 massive gravity decoupling limit theory. Although it is known that the double copy of a nonlinear sigma model is a special Galileon, the decoupling limit of massive Yang-Mills theory is a more general Galileon theory. This demonstrates that the decoupling limit and double copy procedures do not commute and we clarify why this is the case in terms of the scaling of their kinematic factors.

scholarly journals Off-Shell Noether Currents and Potentials for First-Order General Relativity

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 348
Author(s):  
Merced Montesinos ◽  
Diego Gonzalez ◽  
Rodrigo Romero ◽  
Mariano Celada
Keyword(s):  
General Relativity ◽  
Vector Fields ◽  
Killing Vector ◽  
Spherically Symmetric ◽  
Killing Vector Fields ◽  
Arbitrary Vector ◽  
Four Dimensions ◽  
First Order ◽  
Direct Form ◽  
Definition Of

We report off-shell Noether currents obtained from off-shell Noether potentials for first-order general relativity described by n-dimensional Palatini and Holst Lagrangians including the cosmological constant. These off-shell currents and potentials are achieved by using the corresponding Lagrangian and the off-shell Noether identities satisfied by diffeomorphisms generated by arbitrary vector fields, local SO(n) or SO(n−1,1) transformations, ‘improved diffeomorphisms’, and the ‘generalization of local translations’ of the orthonormal frame and the connection. A remarkable aspect of our approach is that we do not use Noether’s theorem in its direct form. By construction, the currents are off-shell conserved and lead naturally to the definition of off-shell Noether charges. We also study what we call the ‘half off-shell’ case for both Palatini and Holst Lagrangians. In particular, we find that the resulting diffeomorphism and local SO(3,1) or SO(4) off-shell Noether currents and potentials for the Holst Lagrangian generically depend on the Immirzi parameter, which holds even in the ‘half off-shell’ and on-shell cases. We also study Killing vector fields in the ‘half off-shell’ and on-shell cases. The current theoretical framework is illustrated for the ‘half off-shell’ case in static spherically symmetric and Friedmann–Lemaitre–Robertson–Walker spacetimes in four dimensions.

scholarly journals Chiral correlators in $$ \mathcal{N} $$ = 2 superconformal quivers

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Francesco Galvagno ◽  
Michelangelo Preti
Keyword(s):  
Field Theory ◽  
Perturbation Theory ◽  
Flat Space ◽  
Field Theories ◽  
Superconformal Field Theories ◽  
Four Dimensions ◽  
Yang Mills ◽  
The Matrix ◽  
Superspace Formalism ◽  
Model Approach

Abstract We consider a family of $$ \mathcal{N} $$ N = 2 superconformal field theories in four dimensions, defined as ℤq orbifolds of $$ \mathcal{N} $$ N = 4 Super Yang-Mills theory. We compute the chiral/anti-chiral correlation functions at a perturbative level, using both the matrix model approach arising from supersymmetric localisation on the four-sphere and explicit field theory calculations on the flat space using the $$ \mathcal{N} $$ N = 1 superspace formalism. We implement a highly efficient algorithm to produce a large number of results for finite values of N , exploiting the symmetries of the quiver to reduce the complexity of the mixing between the operators. Finally the interplay with the field theory calculations allows to isolate special observables which deviate from $$ \mathcal{N} $$ N = 4 only at high orders in perturbation theory.

THE GRAVITATIONAL ORIGIN OF THE DISTINCTION BETWEEN SPACE AND TIME

2009 ◽  
Vol 18 (14) ◽  
pp. 2155-2158 ◽  
Author(s):  
ASHER YAHALOM
Keyword(s):  
General Relativity ◽  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Flat Space ◽  
Gravitational Theory ◽  
Clear Distinction ◽  
Temporal Dimension ◽  
Spatial Dimensions ◽  
Standard Presentation

To the ordinary human it is obvious that there is a clear distinction between the spatial dimensions, in which one can go either way, and the temporal dimension, in which one seems only to move forward. But the uniqueness of time is also rooted in the standard presentation of general relativity, in which the metric of space–time is locally Lorentzian, i.e. ημν = diag (1, -1, -1, -1). This is presented as an independent axiom of the theory, which cannot be deduced. In this essay I will claim otherwise. I will show that the existence of time should not be enforced on the gravitational theory of general relativity but rather should be deduced from it. The method of choice is linear stability analysis of flat space–times.

scholarly journals Effective field theory, past and future

2016 ◽  
Vol 31 (06) ◽  
pp. 1630007 ◽  
Author(s):  
Steven Weinberg
Keyword(s):  
Field Theory ◽  
General Relativity ◽  
Effective Field Theories ◽  
Standard Model ◽  
Effective Field Theory ◽  
Effective Field ◽  
Field Theories ◽  
Strong Interactions ◽  
The Standard Model ◽  
Theory Of Gravitation

I reminisce about the early development of effective field theories of the strong interactions, comment briefly on some other applications of effective field theories, and then take up the idea that the Standard Model and General Relativity are the leading terms in an effective field theory. Finally, I cite recent calculations that suggest that the effective field theory of gravitation and matter is asymptotically safe.

scholarly journals A New Weighted-learning Approach for Exploiting Data Sparsity in Tag-based Item Recommendation Systems

2021 ◽  
Vol 14 (1) ◽  
pp. 387-399
Author(s):  
Noor Ifada ◽  
◽  
Richi Nayak ◽  
Keyword(s):  
Recommendation System ◽  
Recommendation Systems ◽  
Learning Approach ◽  
Tensor Model ◽  
Learning Approaches ◽  
Data Sparsity ◽  
Tensor Models ◽  
Sparsity Problem ◽  
Weighted Rank

The tag-based recommendation systems that are built based on tensor models commonly suffer from the data sparsity problem. In recent years, various weighted-learning approaches have been proposed to tackle such a problem. The approaches can be categorized by how a weighting scheme is used for exploiting the data sparsity – like employing it to construct a weighted tensor used for weighing the tensor model during the learning process. In this paper, we propose a new weighted-learning approach for exploiting data sparsity in tag-based item recommendation system. We introduce a technique to represent the users’ tag preferences for leveraging the weighted-learning approach. The key idea of the proposed technique comes from the fact that users use different choices of tags to annotate the same item while the same tag may be used to annotate various items in tag-based systems. This points out that users’ tag usage likeliness is different and therefore their tag preferences are also different. We then present three novel weighting schemes that are varied in manners by how the ordinal weighting values are used for labelling the users’ tag preferences. As a result, three weighted tensors are generated based on each scheme. To implement the proposed schemes for generating item recommendations, we develop a novel weighted-learning method called as WRank (Weighted Rank). Our experiments show that considering the users' tag preferences in the tensor-based weightinglearning approach can solve the data sparsity problem as well as improve the quality of recommendation.

scholarly journals Rotating Melvin-like Universes and Wormholes in General Relativity

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1306
Author(s):  
Kirill Bronnikov ◽  
Vladimir Krechet ◽  
Vadim Oshurko
Keyword(s):  
Magnetic Field ◽  
General Relativity ◽  
Equation Of State ◽  
Symmetry Axis ◽  
Energy Condition ◽  
Flat Space ◽  
Stiff Matter ◽  
Cylindrically Symmetric ◽  
The One ◽  
The Magnetic Field

We find a family of exact solutions to the Einstein–Maxwell equations for rotating cylindrically symmetric distributions of a perfect fluid with the equation of state p=wρ (|w|<1), carrying a circular electric current in the angular direction. This current creates a magnetic field along the z axis. Some of the solutions describe geometries resembling that of Melvin’s static magnetic universe and contain a regular symmetry axis, while some others (in the case w>0) describe traversable wormhole geometries which do not contain a symmetry axis. Unlike Melvin’s solution, those with rotation and a magnetic field cannot be vacuum and require a current. The wormhole solutions admit matching with flat-space regions on both sides of the throat, thus forming a cylindrical wormhole configuration potentially visible for distant observers residing in flat or weakly curved parts of space. The thin shells, located at junctions between the inner (wormhole) and outer (flat) regions, consist of matter satisfying the Weak Energy Condition under a proper choice of the free parameters of the model, which thus forms new examples of phantom-free wormhole models in general relativity. In the limit w→1, the magnetic field tends to zero, and the wormhole model tends to the one obtained previously, where the source of gravity is stiff matter with the equation of state p=ρ.

Sign in / Sign up

Export Citation Format

Share Document