Strings as perturbations of evolving spin-networks

TL;DR

Smolin constructs a bridge between non-perturbative spin-network dynamics and perturbative string theory by showing that perturbations of causal histories are described by a 1+1 dimensional spin system on timelike surfaces, with leading action proportional to the surface area in the Minkowski limit, corresponding to the bosonic string Nambu action. This 1+1D theory generalizes to quantum groups $G_q$ and yields a concrete criterion: a good classical limit demands a stable, conformally invariant sector in the induced string-like theory. The framework reduces the problem of quantum gravity to analyzing a 2D perturbation theory on embedded surfaces, and provides explicit formulas for perturbation amplitudes and effective actions. If a suitable $G_q$ and amplitudes exist, this approach offers a path to embed gravitons and other massless modes within a discrete, background-independent quantum gravity setting, linking non-perturbative and perturbative descriptions.

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.