Scaling and Renormalization in two dimensional Quantum Gravity

Understand

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.