1998/01/06 by Lee Smolin · 9 citations
Mathematics · Physics and Astronomy · Social Sciences · #Algebraic and Geometric Analysis #International Science and Diplomacy #Limit (mathematics) #Minkowski space #Noncommutative and Quantum Gravity Theories #Perturbation theory (quantum mechanics) #Quantum gravity #Relationship between string theory and quantum field theory #Spin (aerodynamics) #Spin network #String (physics) #String theory #gr-qc #hep-th
paper · pdf · doi:10.1016/s0920-5632(00)00758-1
published in Nuclear Physics B - Proceedings Supplements 88(1-3), 103-113 (Elsevier BV) · Latex, 18 pages, no figures
arxiv created 1998/01/06 · openalex publication_date 2000/06/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.