scholarly journals Local topological markers in odd dimensions

2021 ◽  
Vol 103 (15) ◽  
Author(s):  
Joseph Sykes ◽  
Ryan Barnett
Keyword(s):  
Odd Dimensions

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.

ADHD and ODD Dimensions: Time Varying Prediction of Internalizing Problems from Childhood to Adolescence

2021 ◽  
pp. 108705472110509
Author(s):  
Felix K. So ◽  
Denise Chavira ◽  
Steve S. Lee
Keyword(s):  
Risk Factors ◽  
Risk Factor ◽  
Oppositional Defiant Disorder ◽  
Internalizing Problems ◽  
Ethnically Diverse ◽  
Time Varying ◽  
Childhood Adhd ◽  
Oppositional Defiant ◽  
Inattention And Hyperactivity ◽  
Odd Dimensions

Objective Although childhood ADHD is a risk factor for internalizing problems, it consists of separable inattention and hyperactivity dimensions that differentially predict outcomes. Oppositional defiant disorder also consists of separable dimensions (i.e., irritable, oppositional), co-occurs with ADHD, and predicts internalizing outcomes. To discern independent associations with internalizing problems, dimensions must be considered simultaneously. Methods Controlling for age, sex, and race, we tested inattention, hyperactivity, irritability, and oppositionality as time-varying predictors of 6 to 7-year prospective change in parent- and teacher-rated internalizing problems in 230 ethnically- diverse (50% Caucasian) 5 to 10 year old youth ( M = 7.4 years, 68% male) with ( n = 120) and without ADHD ( n = 110). Results Escalating inattention and irritability, but not hyperactivity and oppositionality, uniquely predicted internalizing problems. Conclusion These findings suggest that inattention and irritability are unique risk factors for later internalizing problems. These dimensions may catalyze internalizing problems across development and constitute important intervention targets.

CHARACTERIZATION OF SUPER QUASI-EINSTEIN MANIFOLD

2014 ◽  
Vol 60 (1) ◽  
pp. 99-108
Author(s):  
K. Halder ◽  
B. Pal ◽  
A. Bhattacharyya ◽  
T. De
Keyword(s):  
Einstein Manifold ◽  
Odd Dimensions

Abstract In this paper we give characterizations of super quasi-Einstein manifold, mixed super quasi-Einstein manifold and mixed generalized quasi-Einstein manifold for both even and odd dimensions.

scholarly journals HOW TO BYPASS BIRKHOFF THROUGH EXTRA DIMENSIONS: A SIMPLE FRAMEWORK FOR INVESTIGATING THE GRAVITATIONAL COLLAPSE IN VACUUM

2006 ◽  
Vol 15 (12) ◽  
pp. 2217-2222 ◽  
Author(s):  
PIOTR BIZOŃ ◽  
BERND G. SCHMIDT
Keyword(s):  
Gravitational Collapse ◽  
Einstein Equations ◽  
Dimensional System ◽  
Spherically Symmetric ◽  
Asymptotically Flat ◽  
Spherical Collapse ◽  
Geometric Setting ◽  
Birkhoff's Theorem ◽  
Birkhoff’S Theorem ◽  
Odd Dimensions

It is fair to say that our current mathematical understanding of the dynamics of gravitational collapse to a black hole is limited to the spherically symmetric situation and, in fact, even in this case much remains to be learned. The reason is that Einstein's equations become tractable only if they are reduced to a (1 + 1)-dimensional system of partial differential equations. Owing to this technical obstacle, very little is known about the collapse of pure gravitational waves because by Birkhoff's theorem there is no spherical collapse in vacuum. In this essay, we describe a new cohomogeneity-two symmetry reduction of the vacuum Einstein equations in five and higher odd dimensions which evades Birkhoff's theorem and admits time-dependent asymptotically flat solutions. We argue that this model provides an attractive (1 + 1)-dimensional geometric setting for investigating the dynamics of gravitational collapse in vacuum.

Self-duality in odd dimensions

1984 ◽  
Vol 136 (1-2) ◽  
pp. 38-42 ◽  
Author(s):  
P.K. Townsend ◽  
K. Pilch ◽  
P. Van Nieuwenhuizen
Keyword(s):  
Self Duality ◽  
Odd Dimensions

scholarly journals Induced Parity Violation in Odd Dimensions

1994 ◽  
Vol 47 (4) ◽  
pp. 465 ◽  
Author(s):  
R Delbourgo ◽  
AB Waites
Keyword(s):  
Parity Violation ◽  
Mass Term ◽  
Field Theories ◽  
Fermion Mass ◽  
Odd Dimensions

One of the interesting features about field theories in odd dimensions is the induction of parity-violating terms and well-defined finite topological actions via quantum loops if a fermion mass term is originally present and conversely. Aspects of this issue are illustrated for electrodynamics in 2+ 1 and 4+ 1 dimensions.

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