Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 12 (2016), 070, 30 pages      arXiv:1603.01902      https://doi.org/10.3842/SIGMA.2016.070
Contribution to the Special Issue on Tensor Models, Formalism and Applications

Flowing in Group Field Theory Space: a Review

Sylvain Carrozza
Université Bordeaux, LaBRI, UMR 5800, 33400 Talence, France

Received March 08, 2016, in final form July 13, 2016; Published online July 16, 2016

Abstract
We provide a non-technical overview of recent extensions of renormalization methods and techniques to Group Field Theories (GFTs), a class of combinatorially non-local quantum field theories which generalize matrix models to dimension $d \geq 3$. More precisely, we focus on GFTs with so-called closure constraint, which are closely related to lattice gauge theories and quantum gravity spin foam models. With the help of recent tensor model tools, a rich landscape of renormalizable theories has been unravelled. We review our current understanding of their renormalization group flows, at both perturbative and non-perturbative levels.

Key words: group field theory; quantum gravity; quantum field theory; renormalization.

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