scholarly journals EASY HOLOGRAPHY

2013 ◽  
Vol 22 (12) ◽  
pp. 1342013
Author(s):  
HEIKKI ARPONEN
Keyword(s):  
Homogeneous Spaces ◽  
Three Dimensional ◽  
De Sitter ◽  
Asymptotic Symmetry ◽  
Infinite Dimensional ◽  
Higher Dimensional ◽  
Black Hole Information ◽  
Holographic Description ◽  
Area Law

It is argued that the role of infinite-dimensional asymptotic symmetry groups in gravity theories are essential for a holographic description of gravity and possibly to a resolution of the black hole information paradox. I present a simple toy model in two-dimensional hyperbolic/anti-de Sitter (AdS) space and describe, by very elementary considerations, how the asymptotic symmetry group is responsible for the entropy area law. Similar results apply also in three-dimensional AdS space. The failure of the approach in higher-dimensional AdS spaces is explained and resolved by considering other asymptotically noncompact homogeneous spaces.

scholarly journals Charge algebra in Al(A)dSn spacetimes

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Adrien Fiorucci ◽  
Romain Ruzziconi
Keyword(s):  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Three Dimensional ◽  
Dirichlet Boundary Conditions ◽  
Boundary Structure ◽  
Asymptotic Symmetry ◽  
Renormalization Procedure ◽  
Field Dependent ◽  
Odd Dimensions

Abstract The gravitational charge algebra of generic asymptotically locally (A)dS spacetimes is derived in n dimensions. The analysis is performed in the Starobinsky/Fefferman-Graham gauge, without assuming any further boundary condition than the minimal falloffs for conformal compactification. In particular, the boundary structure is allowed to fluctuate and plays the role of source yielding some symplectic flux at the boundary. Using the holographic renormalization procedure, the divergences are removed from the symplectic structure, which leads to finite expressions. The charges associated with boundary diffeomorphisms are generically non-vanishing, non-integrable and not conserved, while those associated with boundary Weyl rescalings are non-vanishing only in odd dimensions due to the presence of Weyl anomalies in the dual theory. The charge algebra exhibits a field-dependent 2-cocycle in odd dimensions. When the general framework is restricted to three-dimensional asymptotically AdS spacetimes with Dirichlet boundary conditions, the 2-cocycle reduces to the Brown-Henneaux central extension. The analysis is also specified to leaky boundary conditions in asymptotically locally (A)dS spacetimes that lead to the Λ-BMS asymptotic symmetry group. In the flat limit, the latter contracts into the BMS group in n dimensions.

scholarly journals Non-Commutative Integration of the Dirac Equation in Homogeneous Spaces

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1867
Author(s):  
Alexander Breev ◽  
Alexander Shapovalov
Keyword(s):  
Dirac Equation ◽  
Exact Solutions ◽  
Homogeneous Space ◽  
Integration Method ◽  
Homogeneous Spaces ◽  
Separation Of Variables ◽  
General Structure ◽  
Three Dimensional ◽  
De Sitter ◽  
Elementary Functions

We develop a non-commutative integration method for the Dirac equation in homogeneous spaces. The Dirac equation with an invariant metric is shown to be equivalent to a system of equations on a Lie group of transformations of a homogeneous space. This allows us to effectively apply the non-commutative integration method of linear partial differential equations on Lie groups. This method differs from the well-known method of separation of variables and to some extent can often supplement it. The general structure of the method developed is illustrated with an example of a homogeneous space which does not admit separation of variables in the Dirac equation. However, the basis of exact solutions to the Dirac equation is constructed explicitly by the non-commutative integration method. In addition, we construct a complete set of new exact solutions to the Dirac equation in the three-dimensional de Sitter space-time AdS3 using the method developed. The solutions obtained are found in terms of elementary functions, which is characteristic of the non-commutative integration method.

scholarly journals Critical Combinations of Higher-Order Terms in Einstein-Maxwell Theory and Compactification

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Nahomi Kan ◽  
Kiyoshi Shiraishi
Keyword(s):  
Higher Order ◽  
De Sitter ◽  
Spontaneous Compactification ◽  
Maxwell Theory ◽  
Higher Derivative ◽  
Higher Dimensional ◽  
Inflationary Phase ◽  
Expansion Time ◽  
Higher Order Terms

We discuss the role of a particular combination of higher derivative terms in higher dimensional theories, particularly in the background of spontaneous compactification. Two classes of theories are proposed in this paper. The first model as a generalization of the critical gravity with the Maxwell field could have a de Sitter solution. We consider the Lanczos-Lovelock term and Horndeski term as well as the higher-order Maxwell term for the second model, which contains a possible longer expansion time for the inflationary phase. It is interesting that both models can be regarded as the generalization of the Randjbar-Daemi, Salam and Strathdee (RSS) model and give the well behavior for inflation stage under the specific assumptions.

scholarly journals SUPERALGEBRA OF HIGHER SPINS AND AUXILIARY FIELDS

1988 ◽  
Vol 03 (12) ◽  
pp. 2983-3010 ◽  
Author(s):  
E.S. FRADKIN ◽  
M.A. VASILIEV
Keyword(s):  
Lie Algebras ◽  
De Sitter ◽  
Infinite Dimensional ◽  
Direct Sum ◽  
Finite Dimensional ◽  
Operator Realization ◽  
Simple Operator ◽  
Higher Spins ◽  
Massless Fields

An infinite-dimensional non-Abelian superalgebra is constructed, denoted as shsa(1), which gives rise at the linearized level to linearized curvatures of both massless and auxiliary fields, suggested previously by one of us (M.V.). Various properties of shsa(1) are analysed in detail. Specifically, subalgebras of shsa(1) are found which pretend themselves for the role of independent superalgebras of higher spins and auxiliary fields. A simple operator realization of shsa(1) is presented. P-reversal automorphisms are constructed. N=2 anti-de Sitter superalgebra osp(2, 4) is shown to be a maximal finite-dimensional subalgebra of shsa(1)/o(2). It is observed that the even (boson) subalgebra of shsa(1) decomposes into the direct sum of two infinite-dimensional Lie algebras each giving rise to massless fields of all integer spins. Possible physical implications of this fact are discussed briefly.

Nonlinear Feedback in a Five-Dimensional Lorenz Model

2014 ◽  
Vol 71 (5) ◽  
pp. 1701-1723 ◽  
Author(s):  
Bo-Wen Shen
Keyword(s):  
Numerical Solutions ◽  
Three Dimensional ◽  
Solution Stability ◽  
Nonlinear Feedback ◽  
Lorenz Model ◽  
Dissipative Term ◽  
Higher Dimensional ◽  
The Impact ◽  
Underlying Processes

Abstract In this study, based on the number of modes, the original three-dimensional Lorenz model (3DLM) is generalized with two additional modes [five-dimensional Lorenz model (5DLM)] to examine their role in the predictability of the numerical solutions and to understand the underlying processes that increase the solution stability. As a result of the simplicity of the 5DLM with respect to existing generalized Lorenz models (LMs), the author is able to obtain the analytical solutions of its critical points and identify the role of the major nonlinear term in the solution’s stability, which have previously not been documented in the literature. The nonlinear Jacobian terms of the governing equations are analyzed to highlight the importance of selecting new modes for extending the nonlinear feedback loop of the 3DLM and thus effectively increasing the degree of nonlinearity (i.e., the nonlinear mode–mode interactions) in the 5DLM. It is then shown that numerical solutions in the 5DLM require a larger normalized Rayleigh number r for the onset of chaos and are more predictable than those in the 3DLM when r is between 25 and 40 and the Prandtl number σ is 10. The improved predictability is attributable to the negative nonlinear feedback enabled by the new modes. The role of the (negative) nonlinear feedback is further verified using a revised 3DLM with a parameterized nonlinear eddy dissipative term. The finding of the increased stability in the 5DLM and revised 3DLM with respect to the 3DLM is confirmed with the linear stability analysis and the analysis of the Lyapunov exponents using different values of r and σ. To further understand the impact of an additional heating term, results from the 5DLM and a higher-dimensional LM [e.g., the six-dimensional LM (6DLM)] are analyzed and compared.

The Role of Three-Dimensional Imaging in Evaluation of the Sinonasal Mass

1996 ◽  
Vol 34 (1) ◽  
pp. 27
Author(s):  
Sue Yon Shim ◽  
Ki Joon Sung ◽  
Young Ju Kim ◽  
In Soo Hong ◽  
Myung Soon Kim ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Three Dimensional Imaging ◽  
Sinonasal Mass

Homogenization and Mass Identity vs. Individual Identity. An Analysis in the Light of the Theory of “The Three Dimensional Spiral of Sense

2016 ◽  
Vol 2 (2) ◽  
pp. 40
Author(s):  
Miriam Aparicio
Keyword(s):  
Three Dimensional ◽  
Individual Identity ◽  
Cognitive Effects ◽  
The Media

This study tests some hypotheses included in the psycho-social-communicational paradigm, which emphasizes the cognitive effects of the media and the role of the psychosocial subject as the recipient

Dysregulation of HOX as a Potential Therapeutic Target in Breast Cancer

2020 ◽  
Vol 27 ◽  
Author(s):  
Ji-Yeon Lee ◽  
Myoung Hee Kim
Keyword(s):  
Breast Cancer ◽  
Hox Genes ◽  
Therapeutic Potential ◽  
Expression Patterns ◽  
Genome Structure ◽  
Control Cell ◽  
Three Dimensional ◽  
Cellular Processes ◽  
Hox Protein

: HOX genes belong to the highly conserved homeobox superfamily, responsible for the regulation of various cellular processes that control cell homeostasis, from embryogenesis to carcinogenesis. The abnormal expression of HOX genes is observed in various cancers, including breast cancer; they act as oncogenes or as suppressors of cancer, according to context. In this review, we analyze HOX gene expression patterns in breast cancer and examine their relationship, based on the three-dimensional genome structure of the HOX locus. The presence of non-coding RNAs, embedded within the HOX cluster, and the role of these molecules in breast cancer have been reviewed. We further evaluate the characteristic activity of HOX protein in breast cancer and its therapeutic potential.

Central ossifying fibroma of mandible

2020 ◽  
Vol 13 (12) ◽  
pp. e239286
Author(s):  
Kumar Nilesh ◽  
Prashant Punde ◽  
Nitin Shivajirao Patil ◽  
Amol Gautam
Keyword(s):  
Fibrous Tissue ◽  
Three Dimensional ◽  
Facial Asymmetry ◽  
Ossifying Fibroma ◽  
Mandible Reconstruction ◽  
Three Dimensional Printing ◽  
Osseous Lesion ◽  
Large Size ◽  
Dimensional Printing

Ossifying fibroma (OF) is a rare, benign, fibro-osseous lesion of the jawbone characterised by replacement of the normal bone with fibrous tissue. The fibrous tissue shows varying amount of calcified structures resembling bone and/or cementum. The central variant of OF is rare, and shows predilection for mandible among the jawbone. Although it is classified as fibro-osseous lesion, it clinically behaves as a benign tumour and can grow to large size, causing bony swelling and facial asymmetry. This paper reports a case of large central OF of mandible in a 40-year-old male patient. The lesion was treated by segmental resection of mandible. Reconstruction of the surgical defect was done using avascular fibula bone graft. Role of three-dimensional printing of jaw and its benefits in surgical planning and reconstruction are also highlighted.

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