Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5499933 | Journal of Geometry and Physics | 2017 | 35 Pages |
Abstract
Rooted in group field theory and matrix models, random tensor models are a recent background-invariant approach to quantum gravity in arbitrary dimensions. Colored tensor models (CTM) generate random triangulated orientable (pseudo)-manifolds. We analyze, in low dimensions, which known spaces are triangulated by specific CTM interactions. As a tool, we develop the graph-encoded surgery that is compatible with the quantum-field-theory-structure and use it to prove that a single model, the complex Ï4-interaction in rank-2, generates all orientable 2-bordisms, thus, in particular, also all orientable, closed surfaces. We show that certain quartic rank-3 CTM, the Ï34-theory, has as boundary sector all closed, possibly disconnected, orientable surfaces. Hence all closed orientable surfaces are cobordant via manifolds generated by the Ï34-theory.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
Carlos I. Pérez-Sánchez,