Group Field Theory (GFT) deals with field theory over group space for instance

$$S_2 = \int dg_1dg_2 \mathcal{K}(g_1, g_2)\phi(g_1)\phi(g_2) +\int dg_1dg_2dg_3\mathcal{V}(g_1, g_2, g_3)\phi(g_1)\phi(g_2)\phi(g_3) $$ is a group field theory over some group $G$ with $g_i \in G$ and $\phi:g \to \text{R}$. I would like to know how is the conformal dimension of the field $\phi$ defined in this context. Or is the conformal dimension here a sensible quantity? If it is, how do I write a GFT which is invariant under scaling of the group elements $g$?


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