Related papers: Tensor models and group field theories: combinator…
One of the challenging problems in the condensed matter physics is to understand the quantum many-body systems, especially, their physical mechanisms behind. Since there are only a few complete analytical solutions of these systems, several…
Large-$N$ renormalization group equations for one- and two-matrix models are derived. The exact renormalization group equation involving infinitely many induced interactions can be rewritten in a form that has a finite number of coupling…
We report recent progress on the application of the tensor renormalization group (TRG) to quantum field theories pursued by the Tsukuba group. We explain how to treat the scalar, fermion, and gauge theories with the TRG method presenting…
The tensor renormalization group method is a promising approach to lattice field theories, which is free from the sign problem unlike standard Monte Carlo methods. One of the remaining issues is the application to gauge theories, which is…
In this talk I will present some of the main difficulties we encounter in studying the large scale behavior of disordered systems. This presentation will be done using a field theory language. The difficulties in applying the standard…
Natural linear and coalgebra transformations of tensor algebras are studied. The representations of certain combinatorial groups are given. These representations are connected to natural transformations of tensor algebras and to the groups…
Exact many-body quantum problems are known to be computationally hard due to the exponential scaling of the numerical resources required. Since the advent of the Density Matrix Renormalization Group, it became clear that a successful…
Recurrent neural networks (RNNs) are powerful tools for sequential modeling, but typically require significant overparameterization and regularization to achieve optimal performance. This leads to difficulties in the deployment of large…
Group Field Theories, a generalization of matrix models for 2d gravity, represent a 2nd quantization of both loop quantum gravity and simplicial quantum gravity. In this paper, we construct a new class of Group Field Theory models, for any…
It was recently argued that quantum field theories possess one-form and higher-form symmetries, labelled `generalized global symmetries.' In this paper, we describe how those higher-form symmetries can be understood mathematically as…
Group field theory is a background-independent approach to quantum gravity whose starting point is the definition of a quantum field theory on an auxiliary group manifold (not interpreted as spacetime, but rather as the finite-dimensional…
We construct N-complexes of non completely antisymmetric irreducible tensor fields on $\mathbb R^D$ generalizing thereby the usual complex (N=2) of differential forms. These complexes arise naturally in the description of higher spin gauge…
Quantum renormalization group scheme provides a microscopic understanding of holography through a general mapping between the beta functions of underlying quantum field theories and the holographic actions in the bulk. We show that the…
Modular tensor categories are generalizations of the representation categories of quantum groups at roots of unity axiomatizing the properties necessary to produce 3-dimensional TQFTs. Although other constructions have since been found,…
Very high energy physics needs a coherent description of the four fundamental forces. Non-commutative geometry is a promising mathematical framework which already allowed to unify the general relativity and the standard model, at the…
We show that the large N reduction holds on group manifolds. Large N field theories defined on group manifolds are equivalent to some corresponding matrix models. For instance, gauge theories on S^3 can be regularized in a gauge invariant…
This paper gives a summary of the author's works concerning the emergent general relativity in a particular class of tensor models, which possess Gaussian classical solutions. In general, a classical solution in a tensor model may be…
Lattice regularization is a standard technique for the nonperturbative definition of a quantum theory of fields. Several approaches to the construction of a quantum theory of gravity adopt this technique either explicitly or implicitly. A…
A general framework for effective theories propagating two tensor and one scalar degrees of freedom is investigated. Geometrically, it describes dynamical foliation of spacelike hypersurfaces coupled to a general background, in which the…
We classify the unitary, renormalizable, Lorentz violating quantum field theories of interacting scalars and fermions, obtained improving the behavior of Feynman diagrams by means of higher space derivatives. Higher time derivatives are not…