Summing over all Topologies in CDT String Field Theory

TL;DR

This paper develops a nonperturbative continuum string field theory for 2D quantum gravity via causal dynamical triangulations, enabling a closed-form sum over all topologies and explicit correlation functions.

Contribution

It introduces a matrix-model formulation that allows summing over all topologies in CDT string field theory in closed form, providing new nonperturbative insights.

Findings

Closed-form sum over all genera achieved

Explicit formulas for n-loop correlation functions derived

Establishes parallels with Euclidean quantum gravity approaches

Abstract

By explicitly allowing for topology to change as a function of time, two-dimensional quantum gravity defined through causal dynamical triangulations gives rise to a new continuum string field theory. Within a matrix-model formulation we show that -- rather remarkably -- the associated sum over all genera can be performed in closed form, leading to a nonperturbative definition of CDT string field theory. We also obtain explicit formulas for the n-loop correlation functions. Our construction exhibits interesting parallels with previous, purely Euclidean treatments.