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Functional Renormalisation Group analysis of a Tensorial Group Field Theory on $\mathbb{R}^3$
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abstract
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.
Forward citations
Cited by 2 Pith papers
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Multiple-Order Tensor Field Theory: Enumeration of unitary invariant observables
A Burnside-based enumeration formula, Theorem 4, counts unitary invariant tensor contractions built from fields of multiple orders, recovers known fixed-order counts as a special case, and generates new integer sequences.
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Ward-constrained melonic renormalization group flow for the rank-four $\phi^6$ tensorial group field theory
For the rank-4 φ6 tensorial group field theory, the authors derive a Ward-constrained renormalization group flow and report a nontrivial fixed point, but the fixed point's reported values violate their own consistency...
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