Tensor models and embedded Riemann surfaces

Abstract

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 coloured 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 re-express the Boulatov model as a quantum field theory on these Riemann surfaces.

9 pages, 7 fig

References in corpus (4)

• The 1/N expansion of colored tensor models in arbitrary dimension
• The 1/N expansion of colored tensor models
• Group field theory renormalization - the 3d case: power counting of divergences
• Scaling behaviour of three-dimensional group field theory

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