Quantum $R^2$ Gravity in Two Dimensions

Abstract

Two-dimensional quantum gravity with an $R^2$ 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 $exp\{-2\pi (1-h{)}^2/(m^{2}A)\}$, where $1/m^2$ is the coefficient (times $32\pi$) of $R^2$ and $h$ is the genus of the surface. Although positivity is violated, at a short distance scale ( $\ll 1/m$) surfaces are smooth and the problem of the branched polymer is avoided.

12 pages, latex KEK-TH-355, KEK preprint 92-212, UT-634

References in corpus (2)

• String Model with Dynamical Geometry and Torsion
• A continuum string model for $D>1$

Cited by in corpus (34)

• Character Expansion Methods for Matrix Models of Dually Weighted Graphs
• Geometric Interpretation and Classification of Global Solutions in Generalized Dilaton Gravity
• Exact Solution of Discrete Two-Dimensional R^2 Gravity
• Dirac Quantization Gravity-Yang-Mills Systems in 1+1 Dimensions
• Gravitational Actions in Two Dimensions and the Mabuchi Functional
• Failure of the Regge approach in two dimensional quantum gravity
• Pareto law and Pareto index in the income distribution of Japanese companies
• On Higher Derivative Gravity in Two Dimensions
• Affine Strings
• Fractal Structure with a Typical Scale
• Measuring the string susceptibility in 2D simplicial quantum gravity using the Regge approach
• Two-dimensional Lifshitz-like AdS black holes in $F(R)$ gravity
• Classical Solution of Two Dimensional $R^2$-Gravity and Cross-Over Phenomenon
• Notes on conformal theory with nonprimary energy-momentum tensor that applies to the Nambu-Goto string
• Relations between a typical scale and averages in the breaking of fractal distribution
• Fixed versus random triangulations in 2D simplicial Regge calculus
• Opus on conformal symmetry of the Nambu-Goto versus Polyakov strings
• Towards Quantum Cosmology without Singularities
• 2D Quantum Gravity -Three States of Surfaces-
• All-Order Quantum Gravity in Two Dimensions
• Quantized 2d Dilaton Gravity and Black Holes
• Extrinsic Hermitian Geometry of Functional Determinants for Vector Subbundles and the Drinfeld--Sokolov Ghost System
• Regge's space-time skeletons and the quantization of 2d gravity
• Field condensations and Noncritical String for c>1
• Wolfgang Kummer and the Vienna School of Dilaton (Super-)Gravity
• Weyl Invariance and Spurious Black Hole in Two-Dimensional Dilaton Gravity
• New results on ${\gamma }_{\mathrm{str}}$ in 2D quantum gravity using Regge calculus
• Simplicial Quantum Gravity on a Randomly Triangulated Sphere
• Induced Chiral Supergravities in 2D
• The Quantization of Anomalous Gauge Field Theory and BRST-invariant Models of Two Dimensional Quantum Gravity
• Drinfeld--Sokolov Gravity
• Quantum reparametrizations in the two-dimensional gravity: a look from 2+$\epsilon$ dimensions
• Quantum Corrections for a Cosmological String Solution
• 2D $R^2$ gravity in weak coupling limit