scholarly journals REGGE GRAVITY FROM SPINFOAMS

2013 ◽  
Vol 22 (02) ◽  
pp. 1350001 ◽  
Author(s):  
ELENA MAGLIARO ◽  
CLAUDIO PERINI
Keyword(s):  
Fine Structure ◽  
Quantum Gravity ◽  
Scaling Limit ◽  
Einstein Equations ◽  
Quantum Corrections ◽  
Semiclassical Regime ◽  
Double Scaling Limit

We consider spinfoam quantum gravity in the flipped limit, which is the double scaling limit γ → 0, j → ∞ with γj = const. , where γ is the Immirzi parameter, j is the spin and γj gives the physical area in Planck units. In this regime the amplitude for a 2-complex becomes effectively an integral over Regge-like metrics and seems to enforce Einstein equations in the semiclassical regime. The Immirzi parameter must be considered as dynamical in the sense that it runs to zero when the fine structure of the foam is averaged. In addition to quantum corrections which vanish for ℏ → 0, we find new corrections due to the discreteness of geometric spectra.

NONPERTURBATIVE 2D QUANTUM GRAVITY VIA SUPERSYMMETRIC STRING

1990 ◽  
Vol 05 (30) ◽  
pp. 2565-2572 ◽  
Author(s):  
MAREK KARLINER ◽  
SASHA MIGDAL
Keyword(s):  
Quantum Gravity ◽  
Ground State ◽  
Scaling Limit ◽  
Linear Ordinary Differential Equation ◽  
Third Order ◽  
Quantum Oscillations ◽  
The Third ◽  
Nonperturbative Solution ◽  
Distribution Of Eigenvalues ◽  
Double Scaling Limit

The Parisi-Marinari suggestion to treat 2d quantum gravity as ground state of the 1d supersymmetric string is elaborated in some detail. The third order linear ordinary differential equation describing in the double scaling limit the distribution of eigenvalues of the random matrix (i.e., the Liouville field) is derived and studied numerically. Unlike the Painlevé equation, our equation leads to continuous spectrum; however, the nonperturbative effects display themselves as quantum oscillations on top of smooth WKB distribution. Nonperturbative solution is free of any ambiguities.

UNIVERSALITY OF THE MATRIX MODEL APPROACH TO TWO-DIMENSIONAL QUANTUM GRAVITY

1991 ◽  
Vol 06 (15) ◽  
pp. 1387-1396
Author(s):  
FREDDY PERMANA ZEN
Keyword(s):  
Quantum Gravity ◽  
Matrix Model ◽  
Scaling Limit ◽  
Numerical Calculations ◽  
Two Dimensional ◽  
Coupled Equations ◽  
The Matrix ◽  
Pure Gravity ◽  
Double Scaling Limit ◽  
Model Approach

Universality with respect to triangulations is investigated in the Hermitian one-matrix model approach to 2-D quantum gravity for a potential containing both even and odd terms, [Formula: see text]. With the use of analytical and numerical calculations, I find that the universality holds and the model describes pure gravity, which leads in the double scaling limit to coupled equations of Painlevé type.

scholarly journals NONPERTURBATIVE 2D QUANTUM GRAVITY AND HAMILTONIANS UNBOUNDED FROM BELOW

1993 ◽  
Vol 08 (07) ◽  
pp. 1259-1281 ◽  
Author(s):  
J. AMBJØRN ◽  
C.F. KRISTJANSEN
Keyword(s):  
Quantum Gravity ◽  
Discrete Spectrum ◽  
Strong Coupling ◽  
Weak Coupling ◽  
Scaling Limit ◽  
Strong Coupling Expansion ◽  
Stochastic Stabilization ◽  
Genus Expansion ◽  
Double Scaling Limit

We show how the stochastic stabilization provides both the weak coupling genus expansion and a strong coupling expansion of 2D quantum gravity. The double scaling limit is described by a Hamiltonian which is unbounded from below, but which has a discrete spectrum.

scholarly journals Characters of irrelevant deformations

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Shouvik Datta ◽  
Yunfeng Jiang
Keyword(s):  
Deformation Parameter ◽  
Central Charge ◽  
Scaling Limit ◽  
Small Deformation ◽  
State Dependent ◽  
Dependent Change ◽  
Left And Right ◽  
Double Scaling Limit

Abstract We analyse the $$ T\overline{T} $$ T T ¯ deformation of 2d CFTs in a special double-scaling limit, of large central charge and small deformation parameter. In particular, we derive closed formulae for the deformation of the product of left and right moving CFT characters on the torus. It is shown that the 1/c contribution takes the same form as that of a CFT, but with rescalings of the modular parameter reflecting a state-dependent change of coordinates. We also extend the analysis for more general deformations that involve $$ T\overline{T} $$ T T ¯ , $$ J\overline{T} $$ J T ¯ and $$ T\overline{J} $$ T J ¯ simultaneously. We comment on the implications of our results for holographic proposals of irrelevant deformations.

scholarly journals THE CRITICAL POINT OF UNORIENTED RANDOM SURFACES WITH A NONEVEN POTENTIAL

1993 ◽  
Vol 08 (06) ◽  
pp. 1139-1152
Author(s):  
M.A. MARTÍN-DELGADO
Keyword(s):  
Free Energy ◽  
Partition Function ◽  
Critical Point ◽  
Discrete Model ◽  
Recursion Relation ◽  
Scaling Limit ◽  
Random Surfaces ◽  
Matrix Ensemble ◽  
Quartic Interaction ◽  
Double Scaling Limit

The discrete model of the real symmetric one-matrix ensemble is analyzed with a cubic interaction. The partition function is found to satisfy a recursion relation that solves the model. The double scaling-limit of the recursion relation leads to a Miura transformation relating the contributions to the free energy coming from oriented and unoriented random surfaces. This transformation is the same kind as found with a quartic interaction.

Can quantum black holes be (q, p)-fermions?

2017 ◽  
Vol 32 (15) ◽  
pp. 1750080 ◽  
Author(s):  
Emre Dil
Keyword(s):  
Black Holes ◽  
Gravitational Field ◽  
Fermi Gas ◽  
Einstein Equations ◽  
Quantum Corrections ◽  
Field Equations ◽  
Gravitational Field Equations ◽  
Entropic Gravity ◽  
Two Parameter

In this study, to investigate the very nature of quantum black holes, we try to relate three independent studies: (q, p)-deformed Fermi gas model, Verlinde’s entropic gravity proposal and Strominger’s quantum black holes obeying the deformed statistics. After summarizing Strominger’s extremal quantum black holes, we represent the thermostatistics of (q, p)-fermions to reach the deformed entropy of the (q, p)-deformed Fermi gas model. Since Strominger’s proposal claims that the quantum black holes obey deformed statistics, this motivates us to describe the statistics of quantum black holes with the (q, p)-deformed fermions. We then apply the Verlinde’s entropic gravity proposal to the entropy of the (q, p)-deformed Fermi gas model which gives the two-parameter deformed Einstein equations describing the gravitational field equations of the extremal quantum black holes obeying the deformed statistics. We finally relate the obtained results with the recent study on other modification of Einstein equations obtained from entropic quantum corrections in the literature.

scholarly journals POLYMER GEOMETRY AT PLANCK SCALE AND QUANTUM EINSTEIN EQUATIONS

1996 ◽  
Vol 05 (06) ◽  
pp. 629-648 ◽  
Author(s):  
ABHAY ASHTEKAR
Keyword(s):  
Quantum Gravity ◽  
Planck Scale ◽  
Coarse Graining ◽  
Space Structure ◽  
Einstein Equations ◽  
Hamiltonian Constraint ◽  
Recent Approach ◽  
Canonical Approach ◽  
Background Fields ◽  
Discrete Spectra

Over the last two years, the canonical approach to quantum gravity based on connections and triads has been put on a firm mathematical footing through the development and application of a new functional calculus on the space of gauge equivalent connections. This calculus does not use any background fields (such as a metric) and thus well-suited to a fully non-perturbative treatment of quantum gravity. Using this framework, quantum geometry is examined. Fundamental excitations turn out to be one-dimensional, rather like polymers. Geometrical observables such as areas of surfaces and volumes of regions are purely discrete spectra. Continuum picture arises only upon coarse graining of suitable semi-classical states. Next, regulated quantum diffeomorphism constraints can be imposed in an anomaly-free fashion and the space of solutions can be given a natural Hilbert space structure. Progress has also been made on the quantum Hamiltonian constraint in a number of directions. In particular, there is a recent approach based on a generalized .Wick transformation which maps solutions to the Euclidean quantum constraints to those of the Lorentzian theory. These developments are summarized. Emphasis is on conveying the underlying ideas and overall pictures rather than technical details.

scholarly journals Quantum Gravity Phenomenology from the Thermodynamics of Spacetime

Universe ◽  
2022 ◽  
Vol 8 (1) ◽  
pp. 50
Author(s):  
Ana Alonso-Serrano ◽  
Marek Liška
Keyword(s):  
Quantum Gravity ◽  
Big Bang ◽  
Einstein Equations ◽  
Logarithmic Term ◽  
Quantum Gravity Phenomenology ◽  
Gravity Effects ◽  
Energy Quantum ◽  
The Big Bang ◽  
Big Bang Singularity ◽  
Modified Dynamics

This work is based on the formalism developed in the study of the thermodynamics of spacetime used to derive Einstein equations from the proportionality of entropy within an area. When low-energy quantum gravity effects are considered, an extra logarithmic term in the area is added to the entropy expression. Here, we present the derivation of the quantum modified gravitational dynamics from this modified entropy expression and discuss its main features. Furthermore, we outline the application of the modified dynamics to cosmology, suggesting the replacement of the Big Bang singularity with a regular bounce.

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