RG flow on random surfaces with handles and closed string field theory

TL;DR

This paper explores the renormalization group flow in two-dimensional gravity-coupled theories, revealing second-order equations, quantum properties with handles, and connections to closed string field theory, suggesting a novel interpretation of string theory as RG flow on random surfaces.

Contribution

It demonstrates that RG flow equations in gravity-coupled 2D theories are second order and incorporate string field theory vertices, proposing a new perspective on string theory as RG flow on random topologies.

Findings

Flow equations are second order in derivatives.

Handles induce quantum mechanical properties in the flow.

Beta functions include elementary higher-genus vertices.

Abstract

The renormalization group flow in two-dimensional field theories that are coupled to gravity has unusual features: First, the flow equations are second order in derivatives. Second, in the presence of handles the flow has quantum mechanical properties. Third, the beta functions contain the elementary higher-genus vertices of closed string field theory. This is demonstrated at simple examples and is applied to derive various results about gravitationally dressed beta functions. The possibility of interpreting closed string field theory as the theory of the renormalization group on random surfaces with random topology is considered.