Renormalizable Group Field Theory beyond melonic diagrams: an example in rank four

Abstract

We prove the renormalizability of a gauge-invariant, four-dimensional GFT model on SU(2), whose defining interactions correspond to necklace bubbles (found also in the context of new large-N expansions of tensor models), rather than melonic ones, which are not renormalizable in this case. The respective scaling of different interactions in the vicinity of the Gaussian fixed point is determined by the renormalization group itself. This is possible because the appropriate notion of canonical dimension of the GFT coupling constants takes into account the detailed combinatorial structure of the individual interaction terms. This is one more instance of the peculiarity (and greater mathematical richness) of GFTs with respect to ordinary local quantum field theories. We also explore the renormalization group flow of the model at the non-perturbative level, using functional renormalization group methods, and identify a non-trivial fixed point in various truncations. This model is expected to have a similar structure of divergences as the GFT models of 4d quantum gravity, thus paving the way to more detailed investigations on them.

30 pages, 15 figures, 2 tables; v2: acknowledgements added; v3: minor modifications (including in the title), matches published version

References in corpus (14)

• Exact evolution equation for the effective potential
• Random tensor models in the large N limit: Uncoloring the colored tensor models
• Functional Renormalisation Group Approach for Tensorial Group Field Theory: a Rank-3 Model
• Invitation to Random Tensors
• Holonomy Spin Foam Models: Definition and Coarse Graining
• Group field theories for all loop quantum gravity
• Towards a phase diagram for spin foams
• Asymptotic safety in three-dimensional SU(2) Group Field Theory: evidence in the local potential approximation
• Enhancing non-melonic triangulations: A tensor model mixing melonic and planar maps
• Discrete Renormalization Group for SU(2) Tensorial Group Field Theory
• Renormalization of an Abelian Tensor Group Field Theory: Solution at Leading Order
• Impact of nonlinear effective interactions on GFT quantum gravity condensates
• Group Field Theory in dimension four minus epsilon
• A review of the large N limit of tensor models

Cited by in corpus (39)

• Correlators in tensor models from character calculus
• Ward identities and combinatorics of rainbow tensor models
• Functional Renormalization Group analysis of rank 3 tensorial group field theory: The full quartic invariant truncation
• Cut and join operator ring in Aristotelian tensor model
• Nonperturbative renormalization group beyond melonic sector: The Effective Vertex Expansion method for group fields theories
• Universal critical behavior in tensor models for four-dimensional quantum gravity
• Ward identity violation for melonic $T^4$-truncation
• From Kronecker to tableau pseudo-characters in tensor models
• Quantum fluctuations in the effective relational GFT cosmology
• Emergent Cosmology from Quantum Gravity in the Lorentzian Barrett-Crane Tensorial Group Field Theory Model
• The Complete Barrett-Crane Model and its Causal Structure
• Phase transitions in TGFT: Functional renormalization group in the cyclic-melonic potential approximation and equivalence to O$(N)$ models
• Towards background independent quantum gravity with tensor models
• Progress in the solving nonperturbative renormalization group for tensorial group field theory
• Inequivalent coherent state representations in group field theory
• Ward-constrained melonic renormalization group flow for the rank-four ${\varphi }^6$ tensorial group field theory
• Ward-constrained melonic renormalization group flow
• Unitary symmetry constraints on tensorial group field theory renormalization group flow
• Thermal representations in group field theory: squeezed vacua and quantum gravity condensates
• Phase transitions in TGFT: a Landau-Ginzburg analysis of Lorentzian quantum geometric models
• Renormalization of group field theories for quantum gravity: new scaling results and some suggestions
• Reliability of the local truncations for the random tensor models renormalization group flow
• Pedagogical comments about nonperturbative Ward-constrained melonic renormalization group flow
• Phase transitions in tensorial group field theories: Landau-Ginzburg analysis of models with both local and non-local degrees of freedom
• Flowing in discrete gravity models and Ward identities: A review
• Renormalization group flow of coupled tensorial group field theories: Towards the Ising model on random lattices
• Tullio Regge's legacy: Regge calculus and discrete gravity
• QFT with Tensorial and Local Degrees of Freedom: Phase Structure from Functional Renormalization
• A Renormalizable SYK-type Tensor Field Theory
• No Ward-Takahashi identity violation for an Abelian tensorial group field theories with closure constraint
• Renormalizable Enhanced Tensor Field Theory: The quartic melonic case
• Stochastic dynamics for Group Field Theories
• Large-$d$ behavior of the Feynman amplitudes for a just-renormalizable tensorial group field theory
• Scale invariance beyond criticality within the mean-field analysis of tensorial field theories
• Quantum Gravity, Hydrodynamics and Emergent Cosmology: A Collection of Perspectives
• Functional renormalization group for $p=2$ like glassy matrices in the planar approximation: II. Ward identities method in the deep IR
• Functional renormalization group for p=2 like glassy matrices in the planar approximation: III. Equilibrium dynamics and beyond
• Anomalous higher order Ward identities in tensorial group field theories without closure constraint
• Phase transitions in TGFT: Landau-Ginzburg analysis of the causally complete Lorentzian Barrett-Crane model