2011/04/28 by James P. Ryan
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Combinatorics #Cosmology and Gravitation Theories #Exact solutions in general relativity #Feynman diagram #Geometry #Graph theory #Group field theory #Mathematical analysis #Mathematical physics #Mathematics #Matrix (chemical analysis) #Noncommutative and Quantum Gravity Theories #Physics #Pure mathematics #Quantum #Quantum field theory #Quantum gravity #Quantum mechanics #Riemann surface #Tensor (intrinsic definition) #Tensor field #Theoretical physics #Triangulation #gr-qc
paper · pdf · doi:10.1103/physrevd.85.024010
9 pages, 7 fig
arxiv created 2011/04/28 · openalex publication_date 2012/01/10 · arxiv updated 2013/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Tensor models and, more generally, group field theories are candidates for higher-dimensional quantum gravity, just as matrix models are in the 2D setting. With the recent advent of a 1/N expansion for colored tensor models, more focus has been given to the study of the topological aspects of their Feynman graphs. Crucial to the aforementioned analysis were certain subgraphs known as bubbles and jackets. We demonstrate in the 3D case that these graphs are generated by matrix models embedded inside the tensor theory. Moreover, we show that the jacket graphs represent (Heegaard) splitting surfaces for the triangulation dual to the Feynman graph. With this in hand, we are able to reexpress the Boulatov model as a quantum field theory on these Riemann surfaces.