Nontrivial UV behavior of rank-4 tensor field models for quantum gravity

Abstract

We investigate the universality classes of rank-4 colored bipartite U(1) tensor field models near the Gaussian fixed point with the functional renormalization group. In a truncation that contains all power counting relevant and marginal operators, we find a one-dimensional UV attractor that is connected with the Gaussian fixed point. Hence this is first evidence that the model could be asymptotically safe due to a mechanism similar to the one found in the Grosse-Wulkenhaar model, whose UV behavior near the Gaussian fixed point is also described by one-dimensional attractor that contains the Gaussian fixed point. However, the cancellation mechanism that is responsible for the simultaneous vanishing of the beta functions is new to tensor models, i.e. it does not occur in vector or matrix models.

Latex, 4 pages + references

References in corpus (6)

• Random tensor models in the large N limit: Uncoloring the colored tensor models
• Vanishing of Beta Function of Non Commutative ${\Phi }_4^4$ Theory to all orders
• Functional Renormalisation Group analysis of Tensorial Group Field Theories on ${\mathbb{R}}^d$
• Critical behavior in spherical and hyperbolic spaces
• Towards phase transitions between discrete and continuum quantum spacetime from the Renormalization Group
• Renormalization of an Abelian Tensor Group Field Theory: Solution at Leading Order

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• Tullio Regge's legacy: Regge calculus and discrete gravity
• Renormalizable Enhanced Tensor Field Theory: The quartic melonic case