Classical Solution of Two Dimensional R2-Gravity and Semiclassical Analysis (弦理論と量子重力の課題) (original) (raw)

Classical solution of two dimensional R2-gravity and cross-over phenomenon

Nuclear Physics B, 1995

Two dimensional quantum R 2-gravity and its phase structure are examined in the semiclassical approach and compared with the results of the numerical simulation. Three phases are succinctly characterized by the effective action. A classical solution of R 2-Liouville equation is obtained by use of the solution of the ordinary Liouville equation. The partition function is obtained analytically. A toatal derivative term (surface term) plays an important role there. It is shown that the classical solution can sufficiently account for the cross-over transition of the surface property seen in the numerical simulation.

Quantum R2 gravity in two dimensions

Physics Letters B, 1993

KEK-TH-355 KEK preprint 92-212 UT-634 February 1993 Quantum R 2 Gravity in Two Dimensions

1993

Two-dimensional quantum gravity with an R2 term is investigated in the continuum framework. It is shown that the partition function for small area A is highly suppressed by an exponential factor exp{−2π(1 − h)2/(m2A)}, where 1/m2 is the coefficient (times 32π) of R2 and h is the genus of the surface. Although positivity is violated, at a short distance scale ( ≪ 1/m) surfaces are smooth and the problem of the branched polymer is avoided. kawai@tkyvax.phys.s.u-tokyo.ac.jp nakayama@theory.kek.jp 1 Great progress in the formulation of 2d quantum gravity has been made since the equivalence of 2d quantum gravity and dynamical triangulation (DT)[1] was established. [2] [3] [4] [5] [6] [7] Conformally invariant matters with Virasoro central charge cM ≤ 1 can be consistently coupled to 2d gravity [8] [9] and correlation functions computed in both continuum and DT approaches coincide.[10] The partition function for fixed area A is given by [8] Z(A) = const. AstrM ,h)−3 e μ 2π , (1) where γst...

The Classical Solutions of Two-dimensional Gravity

1999

The solutions of two-dimensional gravity following from a non{ linear Lagrangian L = f(R) p g are classi ed, and their symmetry and singularity properties are described. Then a conformal transformation is applied to rewrite these solutions as analogous solutions of twodimensional Einstein-dilaton gravity and vice versa.

Geometry of a two-dimensional quantum gravity: Numerical study

Nuclear Physics B, 1991

A two-dimensional quantum gravity is simulated by means of the dynamical triangulation model. The size of the lattice was up to hundred thousand triangles. Massively parallel simulations and recursive sampling were implemented independently and produced similar results. Wherever the analytical predictions existed, our results confirmed them. The cascade process of baby universes formulation a la Coleman-Hawking scenario in a two-dimensional case has been observed. We observed that there is a simple universal inclusive probability for a baby universe to appear. This anomalous branching of surfaces led to a rapid growth of the integral curvature inside a circle. The volume of a disk in the internal metric has been proven to grow faster than any power of radius. The scaling prediction for the mean square extent given by the Liouville theory has been confirmed. However, the naive expectation for the average Liouville lagrangian < f (p~6)2 > is about 1 order of magnitude different from the results. This apparently points out to some flaws in the current definition of a Liouville model.

Cylindrically symmetric 2 + 1 gravity in terms of global variables: Quantum dynamics

International Journal of Modern Physics A, 2020

We perform quantization of a model in which gravity is coupled to a circular dust shell in 2 + 1 spacetime dimensions. Canonical analysis shows that momentum space of this model is [Formula: see text]-space, and the global chart for it is provided by the Euler angles. In quantum kinematics, this results in non-commutativity in coordinate space and discreteness of the shell radius in timelike region, which includes the collapse point. At the level of quantum dynamics, we find transition amplitudes between zero and non-zero eigenvalues of the shell radius, which describe the rate of gravitational collapse (bounce). Their values are everywhere finite, which could be interpreted as resolution of the central singularity.

Two dimensional quantum gravity coupled to matter

Physics Letters B, 1992

A classical two dimensional theory of gravity which has a number of interesting features (including a Newtonian limit, black holes and gravitational collapse) is quantized using conformal field theoretic techniques. The critical dimension depends upon Newton's constant, permitting models with d = 4. The constraint algebra and scaling properties of the model are computed.

MINBU Distribution of Two-Dimensional Quantum Gravity: Simulation Result and Semiclassical Analysis

International Journal of Modern Physics A, 1997

We analyze the MINBU distribution of two-dimensional quantum gravity. New data of R2-gravity by the Monte Carlo simulation and its theoretical analysis by the semiclassical approach are presented. In the distribution, the cross-over phenomenon takes place at some size of the baby universe where the randomness competes with the smoothing (or roughening) force of R2-term. The dependence on the central charge cm and on the R2-coupling are explained for R2-gravity, which includes the ordinary 2d quantum gravity. The R2-Liouville solution plays the central role in the semiclassical analysis. A total derivative term (surface term) and the infrared regularization play important roles. The surface topology is that of a sphere.

Two-dimensional quantum gravity

This chapter contains a short review the correspondence between large N matrix models and critical phenomena on lattices with fluctuating geometry.

Classical Solution of Two Dimensional R2-Gravity and Semiclassical Analysis (弦理論と量子重力の課題) (original) (raw)

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