scholarly journals Quaternionic and Poisson–Lie structures in three-dimensional gravity: The cosmological constant as deformation parameter

2008 ◽  
Vol 49 (8) ◽  
pp. 083510 ◽  
Author(s):  
C. Meusburger ◽  
B. J. Schroers
Keyword(s):  
Cosmological Constant ◽  
Deformation Parameter ◽  
Three Dimensional ◽  
Dimensional Gravity

scholarly journals Discrete canonical analysis of three-dimensional gravity with cosmological constant

2015 ◽  
Vol 30 (15) ◽  
pp. 1550080
Author(s):  
J. Berra-Montiel ◽  
J. E. Rosales-Quintero
Keyword(s):  
Cosmological Constant ◽  
Constant Curvature ◽  
Three Dimensional ◽  
Canonical Analysis ◽  
Gauge Freedom ◽  
Dimensional Gravity ◽  
Local Symmetries ◽  
Lattice Approach ◽  
Hamiltonian Analysis ◽  
The Continuum

We discuss the interplay between standard canonical analysis and canonical discretization in three-dimensional gravity with cosmological constant. By using the Hamiltonian analysis, we find that the continuum local symmetries of the theory are given by the on-shell space–time diffeomorphisms, which at the action level, correspond to the Kalb–Ramond transformations. At the time of discretization, although this symmetry is explicitly broken, we prove that the theory still preserves certain gauge freedom generated by a constant curvature relation in terms of holonomies and the Gauss's law in the lattice approach.

scholarly journals Cosmological Constant from Condensation of Defect Excitations

Universe ◽  
2018 ◽  
Vol 4 (7) ◽  
pp. 81 ◽  
Author(s):  
Bianca Dittrich
Keyword(s):  
Hilbert Space ◽  
Quantum Gravity ◽  
Cosmological Constant ◽  
Quantum Cosmology ◽  
Condensed Matter ◽  
Three Dimensional ◽  
Class Constraint ◽  
Four Dimensions ◽  
Dimensional Gravity ◽  
Constraint Algebra

A key challenge for many quantum gravity approaches is to construct states that describe smooth geometries on large scales. Here we define a family of (2+1)-dimensional quantum gravity states which arise from curvature excitations concentrated at point like defects and describe homogeneously curved geometries on large scales. These states represent therefore vacua for three-dimensional gravity with different values of the cosmological constant. They can be described by an anomaly-free first class constraint algebra quantized on one and the same Hilbert space for different values of the cosmological constant. A similar construction is possible in four dimensions, in this case the curvature is concentrated along string-like defects and the states are vacua of the Crane-Yetter model. We will sketch applications for quantum cosmology and condensed matter.

scholarly journals 3d gravity in Bondi-Weyl gauge: charges, corners, and integrability

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Marc Geiller ◽  
Christophe Goeller ◽  
Céline Zwikel
Keyword(s):  
Cosmological Constant ◽  
Three Dimensional ◽  
Solution Space ◽  
Base Space ◽  
Central Extensions ◽  
Retarded Time ◽  
Holographic Renormalization ◽  
Dimensional Gravity ◽  
3D Gravity

Abstract We introduce a new gauge and solution space for three-dimensional gravity. As its name Bondi-Weyl suggests, it leads to non-trivial Weyl charges, and uses Bondi-like coordinates to allow for an arbitrary cosmological constant and therefore spacetimes which are asymptotically locally (A)dS or flat. We explain how integrability requires a choice of integrable slicing and also the introduction of a corner term. After discussing the holographic renormalization of the action and of the symplectic potential, we show that the charges are finite, symplectic and integrable, yet not conserved. We find four towers of charges forming an algebroid given by $$ \mathfrak{vir}\oplus \mathfrak{vir}\oplus $$ vir ⊕ vir ⊕ Heisenberg with three central extensions, where the base space is parametrized by the retarded time. These four charges generate diffeomorphisms of the boundary cylinder, Weyl rescalings of the boundary metric, and radial translations. We perform this study both in metric and triad variables, and use the triad to explain the covariant origin of the corner terms needed for renormalization and integrability.

scholarly journals Free partition functions and an averaged holographic duality

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Nima Afkhami-Jeddi ◽  
Henry Cohn ◽  
Thomas Hartman ◽  
Amirhossein Tajdini
Keyword(s):  
Partition Function ◽  
Spectral Gap ◽  
Central Charge ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Partition Functions ◽  
General Constraints ◽  
Dimensional Gravity ◽  
Holographic Duality

Abstract We study the torus partition functions of free bosonic CFTs in two dimensions. Integrating over Narain moduli defines an ensemble-averaged free CFT. We calculate the averaged partition function and show that it can be reinterpreted as a sum over topologies in three dimensions. This result leads us to conjecture that an averaged free CFT in two dimensions is holographically dual to an exotic theory of three-dimensional gravity with U(1)c×U(1)c symmetry and a composite boundary graviton. Additionally, for small central charge c, we obtain general constraints on the spectral gap of free CFTs using the spinning modular bootstrap, construct examples of Narain compactifications with a large gap, and find an analytic bootstrap functional corresponding to a single self-dual boson.

scholarly journals MEASUREMENTS AND INFORMATION IN SPIN FOAM MODELS

2012 ◽  
Vol 27 (28) ◽  
pp. 1250164
Author(s):  
J. MANUEL GARCÍA-ISLAS
Keyword(s):  
Information Theory ◽  
Quantum Gravity ◽  
Cosmological Constant ◽  
Shannon Entropy ◽  
Three Dimensional ◽  
Spin Network ◽  
Spin Foam Models ◽  
Foam Model ◽  
Spin Foam Model ◽  
Spin Foam

In the three-dimensional spin foam model of quantum gravity with a cosmological constant, there exists a set of observables associated with spin network graphs. A set of probabilities is calculated from these observables, and hence the associated Shannon entropy can be defined. We present the Shannon entropy associated with these observables and find some interesting bounded inequalities. The problem relates measurements, entropy and information theory in a simple way which we explain.

scholarly journals Three-dimensional Maxwellian extended Newtonian gravity and flat limit

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Patrick Concha ◽  
Lucrezia Ravera ◽  
Evelyn Rodríguez ◽  
Gustavo Rubio
Keyword(s):  
Cosmological Constant ◽  
Three Dimensional ◽  
Expansion Method ◽  
Gravity Models ◽  
Newtonian Gravity ◽  
Newtonian Theory ◽  
Relativistic Limit ◽  
Expansion Procedure ◽  
Three Space ◽  
Chern Simons

Abstract In the present work we find novel Newtonian gravity models in three space-time dimensions. We first present a Maxwellian version of the extended Newtonian gravity, which is obtained as the non-relativistic limit of a particular U(1)-enlargement of an enhanced Maxwell Chern-Simons gravity. We show that the extended Newtonian gravity appears as a particular sub-case. Then, the introduction of a cosmological constant to the Maxwellian extended Newtonian theory is also explored. To this purpose, we consider the non-relativistic limit of an enlarged symmetry. An alternative method to obtain our results is presented by applying the semigroup expansion method to the enhanced Nappi-Witten algebra. The advantages of considering the Lie algebra expansion procedure is also discussed.

Entrainment and Transport in Idealized Three-Dimensional Gravity Current Simulation

2006 ◽  
Vol 23 (9) ◽  
pp. 1249-1269 ◽  
Author(s):  
Yu-Heng Tseng ◽  
David E. Dietrich
Keyword(s):  
Gravity Current ◽  
Vertical Mixing ◽  
Three Dimensional ◽  
Ocean Model ◽  
Numerical Dissipation ◽  
Good Convergence ◽  
Low Viscosity ◽  
Denmark Strait ◽  
Dimensional Gravity ◽  
Fine Resolution

Abstract A purely z-coordinate Dietrich/Center for Air Sea Technology (DieCAST) ocean model is applied to the Dynamics of Overflow Mixing and Entrainment (DOME) idealized bottom density current problem that is patterned after the Denmark Strait. The numerical results show that the background viscosity plays a more important role than the chosen coordinate system in the entrainment and mixing if the background viscosity is not small enough. Both higher horizontal viscosity and coarser resolution leads to slower along-slope propagation. Reducing vertical mixing parameterization also leads to slower along-slope propagation with thicker plume size vertically. The simulation gives consistent results for the moderate- and fine-resolution runs. At a very coarse grid the dense water descends more slowly and is mainly dominated by diffusion. Time-averaged downstream transport and entrainment are not very sensitive to viscosity after the flow reaches its quasi-steady status. However, more realistic eddies and flow structures are found in low-viscosity runs. The results show good convergence of the resolved flow as expected and clarify the effects of numerical dissipation/mixing on overflow modeling. Larger numerical dissipation is not required nor recommended in z-coordinate models.

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