# A Real-Space Renormalization Group for Random Surfaces

## TL;DR

This paper introduces a novel real-space renormalization group method for dynamical triangulations, preserving key geometrical exponents and identifying fixed points, with results aligning closely with theoretical predictions.

## Contribution

It presents a new RG transformation for dynamical triangulations that maintains geometrical exponents and provides estimates for dressed exponents in coupled gravity-Ising systems.

## Key findings

- Preserves geometrical exponents like string susceptibility and Hausdorff dimension.
- Identifies fixed point structures in pure and coupled gravity models.
- Estimates gravitationally dressed exponents consistent with KPZ formula.

## Abstract

We propose a new real-space renormalization group transformation for dynamical triangulations. It is shown to preserve geometrical exponents such as the string susceptibility and Hausdorff dimension. We furthermore show evidence for a fixed point structure both in pure gravity and gravity coupled to a critical Ising system. In the latter case we are able to extract estimates for the gravitationally dressed exponents which agree to within 2-3% of the KPZ formula.