Strings as perturbations of evolving spin-networks

TL;DR

This paper establishes a link between non-perturbative quantum gravity, modeled via spin networks, and perturbative string theory, showing that perturbations correspond to string-like surfaces with actions proportional to their area.

Contribution

It introduces a novel framework connecting spin network dynamics with string theory through perturbations on discrete spacetime surfaces, extending to quantum groups and supergroups.

Findings

Perturbations of spin network histories resemble string worldsheet actions.

The classical limit corresponds to Minkowski spacetime with a string-like action.

The approach generalizes to various quantum groups and supergroups.

Abstract

A connection between non-perturbative formulations of quantum gravity and perturbative string theory is exhibited, based on a formulation of the non-perturbative dynamics due to Markopoulou. In this formulation the dynamics of spin network states and their generalizations is described in terms of histories which have discrete analogues of the causal structure and many fingered time of Lorentzian spacetimes. Perturbations of these histories turn out to be described in terms of spin systems defined on 2-dimensional timelike surfaces embedded in the discrete spacetime. When the history has a classical limit which is Minkowski spacetime, the action of the perturbation theory is given to leading order by the spacetime area of the surface, as in bosonic string theory. This map between a non-perturbative formulation of quantum gravity and a 1+1 dimensional theory generalizes to a large class of theories in which the group SU(2) is extended to any quantum group or supergroup. It is argued that a necessary condition for the non-perturbative theory to have a good classical limit is that the resulting 1+1 dimensional theory defines a consistent and stable perturbative string theory.