A perturbative approach to chiral induced two-dimensional gravity

In the framework of the covariant approach, based on perturbation theory, two-dimensional chiral induced quantum gravity is analyzed. The quantum equivalence with the local version of two-dimensional induced quantum gravity is established.Lenin Komsemol Tomsk State Pedagogical Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 102–105, December, 1992.     

Some remarks on the Liouville approach to two-dimensional quantum gravity

We show the equivalence of tow-dimensional quantum gravity interacting with a total number of scalar and Dirac-fermion degrees of freedom less of 26 and quantum Liouvill field theory. An analysis of the two-dimensional effective geometry, as well as of the conditions of non-triviality of the resulting quantum theory, is also included. A general procedure to get the complete one-loop effective action is suggested at the end.     

Generalized anti-centrifugal potential

We generalize the quantum anti-centrifugal potential in the two-dimensional Euclidean plane to two-dimensional surfaces embedded in three-dimensional Euclidean space. We consider the sphere with two caps removed in some detail. We show that quantum particles in this space are “pushed” towards either of the cap boundaries. We also consider the two-dimensional Euclidean plane with an elliptic area removed and compute the quantum anti-centrifugal potential on the elliptic boundary. It is argued that a sufficiently thin electrically conducting nano-wire shaped as an ellipse will exhibit an inhomogeneous charge distribution due to this quantum potential.     

Spectroscopy of a canonically quantized horizon

Deviations from Hawking's thermal black hole spectrum, observable for macroscopic black holes, are derived from a model of a quantum horizon in loop quantum gravity. These arise from additional area eigenstates present in quantum surfaces excluded by the classical isolated horizon boundary conditions. The complete spectrum of area unexpectedly exhibits evenly spaced symmetry. This leads to an enhancement of some spectral lines on top of the thermal spectrum. This can imprint characteristic features into the spectra of black hole systems. It most notably gives the signature of quantum gravity observability in radiation from primordial black holes, and makes it possible to test loop quantum gravity with black holes well above Planck scale.     

Multi-matrix models from jet coefficients

We present a very natural framework in which to discuss multi-matrix models of two-dimensional quantum gravity. Multi-matrix model actions, string equations, and other quantities can be compactly expressed in terms of the jets of the resolvents of the relevant differential operators. This allows one to write down equations describing minimal matter coupled to two-dimensional quantum gravity directly in terms of known functionals.     

Modified de Broglie--Bohm approach to the Schwarzschild black hole

A modified de Broglie-Bohm approach is generalized to the Schwarzschild black hole. By using this method, the quantum potential and the quantum trajectories of the black hole are investigated. And we find that the linear combination of two particular solutions of the black hole wavefunction is not physical although each of them is physical, if we think that the quantum gravity should reduce into its corresponding classical counterpart in which the gravity vanishes. It seems to confirm the argument, given by Alwis and MacIntire, that a possible resolution on the quantum gravity is to give up the superposition principle.     

Unique effective action in two-dimensional quantum gravity with nonlocal action

The gauge dependence of the effective action in two-dimensional induced quantum gravity is investigated. A unique effective action is found, and its dependence on the metric of the configuration space is studied.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 97–100, January, 1992.     

Quantum field theory on Riemann surfaces and the unitarity problem

By the use of the Klein method instead of the theta-function method of Jacobi we are able to relate a conformal quantum theory or Riemann surfaces to the corresponding flat-space field theory and its Virasoro algebra. Physical positivity holds on a distinguished real subset in the manifold with nonrivial Hausdorff dimension which in the general case g > 1 cannot be shifted by a hamiltonian. Our picture of obtaining curved two-dimensional quantum field theories by applying a special diffeomorphism to flat ones resembles that of the Hawking-Unruh effect.     

Convenient versus unique effective action formalism in 2d dilaton-Maxwell quantum gravity

The structure of one-loop divergences of two-dimensional dilaton-Maxwell quantum gravity is investigated in two formalisms: one using a convenient effective action and the other a unique effective action. The one-loop divergences (including surface divergences) of the convenient effetive action are calculated in three different covariant gauges: (i) De Witt, (ii) Ω-degenerate De Witt, and (iii) simplest covariant. The on-shell effective action is given by surface divergences only (finiteness of theS-matrix), which yet depend upon the gauge condition choice. Off-shell renormalizability is discussed and classes of renormalizable dilaton and Maxwell potentials are found which coincide in the cases of convenient and unique effective actions. A detailed comparison of both situations, i.e. convenient vs. unique effective action, is given. As an extension of the procedure, the one-loop effective action in two-dimensional dilaton-Yang-Mills gravity is calculated.     

Dynamical method for quantizing gravity and the problem of decoherence in quantum cosmology

A regularized quantum theory of gravity interacting with matter is constructed. The construction is made on the basis of the method of dynamical quantization of generally covariant theories. A solution of the problem of decoherence in quantum cosmology is proposed on the basis of this method.     

Operator product expansion in two-dimensional quantum gravity

We consider correlation functions of operators and the operator product expansion in two-dimensional quantum gravity. First we introduce correlation functions with geodesic distances between operators kept fixed. Next, by making two of the operators closer, we examine whether there exists an analog of the operator product expansion in ordinary field theories. Our results suggest that the operator product expansion holds in quantum gravity as well, though special care should be taken regarding the physical meaning of fixing geodesic distances on a fluctuating geometry.     

Gravity on a multifractal

Despite their diversity, many of the most prominent candidate theories of quantum gravity share the property to be effectively lower-dimensional at small scales. In particular, dimension two plays a fundamental role in the finiteness of these models of Nature. Thus motivated, we entertain the idea that spacetime is a multifractal with integer dimension 4 at large scales, while it is two-dimensional in the ultraviolet. Consequences for particle physics, gravity and cosmology are discussed.     

Geometry of a two-dimensional quantum gravity: Numerical study

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 à 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 ∫(φ)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.     

Random geometry, quantum gravity and the Kähler potential

We propose a new method to define theories of random geometries, using an explicit and simple map between metrics and large hermitian matrices. We outline some of the many possible applications of the formalism. For example, a background-independent measure on the space of metrics can be easily constructed from first principles. Our framework suggests the relevance of a new gravitational effective action and we show that it occurs when coupling the massive scalar field to two-dimensional gravity. This yields new types of quantum gravity models generalizing the standard Liouville case.     

Commensurate oscillations of the magnetoresistance of a two-dimensional electron gas in GaAs quantum wells with corrugated heteroboundaries

Oscillations of the magnetoresistance commensurate with the spatial modulation period of the growth surfaces were observed in selectively doped GaAs quantum wells with AlAs/GaAs superlattice barriers grown by molecular beam epitaxy. The experimental data obtained are explained by the lateral potential modulation of the two-dimensional electron gas in narrow GaAs quantum wells with corrugated heteroboundaries and agree with the two-dimensional distribution of the local capacitance in such structures.     

The emergence of background geometry from quantum fluctuations

We show how the quantization of two-dimensional gravity leads to an (Euclidean) quantum space–time where the average geometry is that of constant negative curvature and where the Hartle–Hawking boundary condition arises naturally.     

A matrix model for 2D quantum gravity defined by Causal dynamical triangulations

A novel continuum theory of two-dimensional quantum gravity, based on a version of Causal Dynamical Triangulations which incorporates topology change, has recently been formulated as a genuine string field theory in zero-dimensional target space [J. Ambjørn, R. Loll, Y. Watabiki, W. Westra, S. Zohren, arXiv: 0802.0719]. Here we show that the Dyson–Schwinger equations of this string field theory are reproduced by a cubic matrix model. This matrix model also appears in the so-called Dijkgraaf–Vafa correspondence if the superpotential there is required to be renormalizable. In the spirit of this model, as well as the original large-N expansion by 't Hooft, we need no special double-scaling limit involving a fine tuning of coupling constants to obtain the continuum quantum-gravitational theory. Our result also implies a matrix model representation of the original, strictly causal quantum gravity model.