Scaling and Renormalization in two dimensional Quantum Gravity

Abstract

We study scaling and renormalization in two dimensional quantum gravity in a covariant framework. After reviewing the definition of a proper path integral measure, we use scaling arguments to rederive the KPZ relations, the fractal dimension of the theory and the scaling of the reparametrization-invariant two point function. Then we compute the scaling exponents entering in this relations by means of the functional RG. We show that a key ingredient to obtain the correct results already known from Liouville theory is the use of the exponential parametrization for metric fluctuations. We also show that with this parametrization we can recover the correct finite part of the effective action as the $\epsilon \to 0$ continuation of gravity in $d=2+\epsilon$ dimensions.

39 pages

References in corpus (3)

• Field Parametrization Dependence in Asymptotically Safe Quantum Gravity
• On the non-local heat kernel expansion
• Towards phase transitions between discrete and continuum quantum spacetime from the Renormalization Group

Cited by in corpus (14)

• The Renormalization Group flow of unimodular f(R) gravity
• Renormalisation of Newton's constant
• Connections and geodesics in the space of metrics
• The background scale Ward identity in quantum gravity
• Physical renormalization schemes and asymptotic safety in quantum gravity
• Vacuum effective actions and mass-dependent renormalization in curved space
• Composite Operators in Asymptotic Safety
• The unitary conformal field theory behind 2D Asymptotic Safety
• Splitting Ward identity
• Split Weyl transformations in quantum gravity
• Gravity in $d=2+\epsilon$ dimensions and realizations of the diffeomorphisms group
• Trace anomaly and infrared cutoffs
• Geometric operators in the asymptotic safety scenario for quantum gravity
• Functional and Local Renormalization Groups