Related papers: Constructive tensor field theory: The $T^{4}_{4}$ …
We extend the technique of constructive expansions to compute the connected functions of matrix models in a uniform way as the size of the matrix increases. This provides the main missing ingredient for a non-perturbative construction of…
The tensor renormalization group attracts great attention as a new numerical method that is free of the sign problem. In addition to this striking feature, it also has an attractive aspect as a coarse-graining of space-time; the…
We study the spectrum of the large $N$ quantum field theory of bosonic rank-$3$ tensors, whose quartic interactions are such that the perturbative expansion is dominated by the melonic diagrams. We use the Schwinger-Dyson equations to…
The nontrivial fixed point discovered for $\phi^4$-marginal couplings in tensorial group field theories have been showed to be incompatible with Ward-Takahashi identities. In this previous analysis we have stated that the case of models…
We study the quantization of the noncommutative selfdual \phi^3 model in 4 dimensions, by mapping it to a Kontsevich model. The model is shown to be renormalizable, provided one additional counterterm is included compared to the…
We study the noncommutative $\phi^4$ theory with spontaneously broken global O(2) symmetry in 4 dimensions. We demonstrate the renormalizability at one loop. This does not require any choice of ordering of the fields in the interaction…
We develop the functional renormalization group formalism for a tensorial group field theory with closure constraint, in the case of an Abelian just renormalizable model with quartic interactions. The method allows us to obtain a closed but…
We consider a scalar $\phi^4$ theory on canonically deformed Euclidean space in 4 dimensions with an additional oscillator potential. This model is known to be renormalisable. An exterior gauge field is coupled in a gauge invariant manner…
Generalizing matrix models, tensor models generate dynamical triangulations in any dimension and support a $1/N$ expansion. Using the intermediate field representation we explicitly rewrite a quartic tensor model as a field theory for a…
This article provides a Wilsonian description of the perturbatively renormalizable Tensorial Group Field Theory introduced in arXiv:1303.6772 [hep-th] (Commun. Math. Phys. 330, 581-637). It is a rank-3 model based on the gauge group SU(2),…
The construction of field theories with space-time symmetries, including tensorial charges (i.e. of M-theory type), initiated in hep-th/9907011, is extended to include interaction. For SO(2,2) gravity in a tensorial space-time, with…
We provide a brief overview of tensor models and group field theories, focusing on their main common features. Both frameworks arose in the context of quantum gravity research, and can be understood as higher-dimensional generalizations of…
We consider a multi-scalar field theory with either short-range or long-range free action and with quartic interactions that are invariant under $O(N_1)\times O(N_2) \times O(N_3)$ transformations, of which the scalar fields form a…
Since Weinberg's proposal two decades ago, chiral effective field theory in the NN sector has been developed and applied up to order $O((Q/M_{hi})^4)$. In principle it could provide a model-independent description of nuclear force from QCD.…
Extending tensor models at the field theoretical level, tensor field theories are nonlocal quantum field theories with Feynman graphs identified with simplicial complexes. They become relevant for addressing quantum topology and geometry in…
The renormalization in a Lorentz-breaking scalar-spinor higher-derivative model involving $\phi^4$ self-interaction and the Yukawa-like coupling is studied. We explicitly de- monstrate that the convergence is improved in comparison with the…
Scalar field theory is studied by constructing interacting saddle point expansions in the symmetric and broken phase, respectively. Focusing on analytically tractable saddle expansions, it is found that broken and symmetric phases are…
For some theories where the degrees of freedom are tensors of rank $3$ or higher, there exist solvable large $N$ limits dominated by the melonic diagrams. Simple examples are provided by models containing one rank-$3$ tensor in the…
This note supplements an earlier paper on conformal field theories. There it was shown how to construct tensor, spinor, and spinor-tensor primary fields in four dimensions from their counterparts in six dimensions, where conformal…
We provide an up-to-date review of the recent constructive program for field theories of the vector, matrix and tensor type, focusing not on the models themselves but on the mathematical tools used.