5 problems

Let $G$ be a graph in the Boulatov model, let $n$ denote the relevant graph order, let $Z_G$ be its amplitude, and let $\Lambda$ be the cutoff parameter. Assume that $G$ has no two…

Let $\mathfrak{J}_{\text{EL}}$ be the set of equilateral configurations and let $\mathfrak{J}_{\text{EL}}^{S}$ denote the subset of configurations for which the relevant $6J$-symbo…

Let $D$ be odd or even, and let $\widetilde{\mathfrak{C}}_{D,coloured}$ be the set of labelled loopless $D$-regular boundary graphs whose edges can be coloured with $D$ colours so…

The colored Boulatov model is a rank-$3$ tensor model whose fields are defined over the group $SU(2)$; its dynamical version includes a Laplacian in the kinetic term, and open grap…

A 3-bubble is a three-dimensional bubble in a group field theory diagram, and its link $L_v$ is the surface encoding the topology around the vertex. The bubble is planar when $L_v$…