Related papers: Scaling and Renormalization in two dimensional Qua…
We perform the two loop level renormalization of quantum gravity in $2+\epsilon$ dimensions. We work in the background gauge whose manifest covariance enables us to use the short distance expansion of the Green's functions. We explicitly…
We discuss some classical and quantum properties of 2d gravity models involving metric and a scalar field. Different models are parametrized in terms of a scalar potential. We show that a general Liouville-type model with exponential…
We prove the renormalizability of quantum gravity near two dimensions. The successful strategy is to keep the volume preserving diffeomorphism as the manifest symmetry of the theory. The general covariance is recovered by further imposing…
We present a (mathematically rigorous) probabilistic and geometrical proof of the KPZ relation between scaling exponents in a Euclidean planar domain D and in Liouville quantum gravity. It uses the properly regularized quantum area measure…
Quantum gravitational effects on the renormalization group equation are studied in the $(2+\epsilon)$-dimensional approach. Divergences in a matter one-loop effective action do not receive gravitational radiative corrections. The…
We study two--loop renormalization in $(2+\epsilon)$--dimensional quantum gravity. As a first step towards the full calculation, we concentrate on the divergences which are proportional to the number of matter fields. We calculate the…
The main part of this presentation is a review of the previous original works on the perturbative covariant approach to the $2$-dimensional quantum gravity. We discuss the renormalization of the two-dimensional dilaton gravity in a harmonic…
We examine the relations between observables in two- and three-dimensional quantum gravity by studying the coupling of topologically massive gravity to matter fields in non-trivial representations of the three-dimensional Lorentz group. We…
We re-examine results of the Liouville theory and provide arguments that a {\it negative} bare cosmological constant is essential to define two-dimensional quantum gravity. From this we are naturally led to a regularization of quantum…
We study the renormalizability of quantum gravity near two dimensions. Our formalism starts with the tree action which is invariant under the volume preserving diffeomorphism. We identify the BRS invariance which originates from the full…
Consider a bounded planar domain D, an instance h of the Gaussian free field on D (with Dirichlet energy normalized by 1/(2\pi)), and a constant 0 < gamma < 2. The Liouville quantum gravity measure on D is the weak limit as epsilon tends to…
The methods of the renormalization group and the $\varepsilon$-expansion are applied to quantum gravity revealing the existence of an asymptotically safe fixed point in spacetime dimensions higher than two. To facilitate this, physical…
We show that there exists a divergent correlation length in 2d quantum gravity for the matter fields close to the critical point provided one uses the invariant geodesic distance as the measure of distance. The corresponding…
We study the Euclidean path integral of two-dimensional quantum gravity with positive cosmological constant coupled to conformal matter with large and positive central charge. The problem is considered in a semiclassical expansion about a…
We propose that the consistent field renormalization of gravity requires a specific Weyl transformation of the metric tensor. As a consequence, proper length and time, as well as energy and momentum, become functions of scale. We estimate…
The main results for the two-dimensional quantum gravity, conjectured from the matrix model or integrable approach, are presented in the form to be compared with the world-sheet or Liouville approach. In spherical limit the integrable side…
Using (2+$\epsilon$)-dimensional quantum gravity recently formulated by Kawai, Kitazawa and Ninomiya, we calculate the scaling dimensions of manifestly generally covariant operators in two-dimensional quantum gravity coupled to $(p,q)$…
We formulate quantum gravity in $2+\epsilon$ dimensions in such a way that the conformal mode is explicitly separated. The dynamics of the conformal mode is understood in terms of the oversubtraction due to the one loop counter term. The…
We consider two-dimensional quantum gravity coupled to matter fields which are renormalizable, but not conformal invariant. Questions concerning the $\b$ function and the effective action are addressed, and the effective action and the…
We consider a model of 2D gravity with the action quadratic in curvature and represent path integrals as integrals over the SL(2, R) invariant Gaussian functional measure. We reduce these path integrals to the products of Wiener path…