Strings as perturbations of evolving spin networks

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.

U Duality and Network Configurations of Branes

“…By varying these and other moduli, including those for internal branes, one can study the non-perturbative aspects of the theory like the coulomb and the Higgs branch and phase transitions between them. Similar kinds of networks have also been found to play crucial roles in various other contexts like quantum gravity and branched polymer [14].…”

Spacetime and the philosophical challenge of quantum gravity

“…If our present understanding of quantum gravity is any guide, this effective quantisation of the gravitational field will involve a non-local-possibly string-like-structure. This raises the intriguing question of whether superstring theory and the loop-variable approach to canonical quantum gravity can both be regarded as different modes-or phases-of a more basic, common structure [43]. A central issue, presumably, is whether supersymmetry can be assigned some significant role in the Ashtekar programme.…”

Spin foam perturbation theory

“…This idea is already present in the work of Freidel and Krasnov [15], who consider a large class of spin foam models as perturbations of BF theory. It is also related to Smolin's work on strings as perturbations of evolving spin networks [30].…”