Functional Renormalisation Group analysis of a Tensorial Group Field Theory on $\mathbb{R}^3$

Understand

We study a model of Tensorial Group Field Theory (TGFT) on $\mathbb{R}^3$ from the point of view of the Functional Renormalisation Group.

• This is the first attempt to apply a renormalisation procedure to a TGFT model defined over a non-compact group manifold.
• IR divergences (with respect to the metric on $\mathbb{R}$) coming from the non-compactness of the group are regularised via compactification, and a thermodynamic limit is then taken.
• We identify then IR and UV fixed points of the RG flow and find strong hints of a phase transition of the TGFT system from a symmetric to a broken or condensate phase in the IR.