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Renormalization of an Abelian Tensor Group Field Theory: Solution at Leading Order
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We study a just renormalizable tensorial group field theory of rank six with quartic melonic interactions and Abelian group U(1). We introduce the formalism of the intermediate field, which allows a precise characterization of the leading order Feynman graphs. We define the renormalization of the model, compute its (perturbative) renormalization group flow and write its expansion in terms of effective couplings. We then establish closed equations for the two point and four point functions at leading (melonic) order. Using the effective expansion and its uniform exponential bounds we prove that these equations admit a unique solution at small renormalized coupling.
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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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