Recent progress in the theory of random surfaces and simplicial quantum gravity

TL;DR

This paper reviews recent advances in the theory of random surfaces and simplicial quantum gravity, covering 2D quantum gravity failures, new behaviors, and higher-dimensional models.

Contribution

It provides an overview of recent developments, including the understanding of the $c>1$ regime, new critical behaviors, and challenges in higher-dimensional models.

Findings

Failure of Regge calculus in 2D quantum gravity

New critical behavior with extrinsic curvature

Discussion on entropy bounds and continuum extraction in higher dimensions

Abstract

Some of the recent developments in the theory of random surfaces and simplicial quantum gravity is reviewed. For 2d quantum gravity this includes the failure of Regge calculus, our improved understanding of the $c>1$ regime, some surprises for q-state Potts models with $q > 4$, attempts to use renormalization group techniques, new critical behavior of random surface models with extrinsic curvature and improved algorithms. For simplicial quantum gravity in higher dimensions it includes a discussion of the exponential entropy bound needed for the models to be well defined, the question of ``computational ergodicity'' and the question of how to extract continuum behavior from the lattice simulations.