Towards phase transitions between discrete and continuum quantum spacetime from the Renormalization Group

TL;DR

This paper uses the functional Renormalization Group to explore a potential phase transition in quantum gravity from a discrete pre-geometric phase to a continuum geometric phase, analyzing fixed points and scheme dependence.

Contribution

It introduces a new approach to study phase transitions in quantum gravity via the Renormalization Group, focusing on multicritical fixed points and scheme reduction techniques.

Findings

Identification of multicritical fixed points related to quantum gravity with matter

Development of an approximation reducing scheme dependence and computational effort

Proposal of a scenario linking the double-scaling limit to continuum quantum gravity fixed points

Abstract

We establish the functional Renormalization Group as an exploratory tool to investigate a possible phase transition between a pre-geometric discrete phase and a geometric continuum phase in quantum gravity. In this paper, based on the analysis of [1], we study three new aspects of the double-scaling limit of matrix models as Renormalization Group fixed points: Firstly, we investigate multicritical fixed points, which are associated with quantum gravity coupled to conformal matter. Secondly, we discuss an approximation that reduces the scheme dependence of our results as well as computational effort while giving good numerical results. This is a consequence of the approximation being a solution to the unitary Ward-identity associated to the U(N) symmetry of the hermitian matrix model. Thirdly, we discuss a scenario that relates the double scaling limit to fixed points of continuum quantum gravity.