Related papers: The 1/N expansion of colored tensor models

Random tensor models are generalizations of random matrix models which admit $1/N$ expansions. In this article we show that the topological recursion, a modern approach to matrix models which solves the loop equations at all orders, is also…

In the present work we have developed a large-N expansion for the $t-J$ model based on the path integral formulation for Hubbard-operators. Our large-N expansion formulation contains diagrammatic rules, in which the propagators and vertex…

In this article we explore the holographic duals of tensor models using collective field theory. We develop a description of the gauge invariant variables of the tensor model. This is then used to develop a collective field theory…

We introduce and briefly analyze the rainbow tensor model where all planar diagrams are melonic. This leads to considerable simplification of the large N limit as compared to that of the matrix model: in particular, what are dressed in this…

We establish new algorithmic guarantees with matching hardness results for coloring and independent set problems in one-sided expanders and related classes of graphs. For example, given a $3$-colorable regular one-sided expander, we compute…

The renormalizability of the three dimensional supersymmetric CP^(N - 1) model is discussed in the 1/N-expansion method, to all orders of 1/N. The model has N copies of the dynamical field and the amplitudes are expanded in powers of 1/N.…

Random tensor models for a generic complex tensor generalize matrix models in arbitrary dimensions and yield a theory of random geometries. They support a 1/N expansion dominated by graphs of spherical topology. Their Schwinger Dyson…

This thesis focuses on renormalization of quantum field theories. Its first part considers three tensor models in three dimensions, a Fermionic quartic with tensors of rank-3 and two Bosonic sextic, of ranks 3 and 5. We rely upon the…

Tensor models are used nowadays for implementing a fundamental theory of quantum gravity. We define here a polynomial $\mathcal T$ encoding the supplementary topological information. This polynomial is a natural generalization of the…

The notion of bounded expansion captures uniform sparsity of graph classes and renders various algorithmic problems that are hard in general tractable. In particular, the model-checking problem for first-order logic is fixed-parameter…

We present a non-perturbative method for the study of the O(N+1)-version of the linear sigma-model. Using boson-mapping techniques, in close analogy to those well-known for fermionic systems, we obtain a systematic 1/N-expansion for the…

We present a new algorithm for finding large independent sets in $3$-colorable graphs with small $1$-sided threshold rank. Specifically, given an $n$-vertex $3$-colorable graph whose uniform random walk matrix has at most $r$ eigenvalues…

We study the tensor model generalization of the quantum $p$-spherical model in the large-$N$ limit. While the tensor model has the same large-$N$ expansion as the disordered quantum $p$-spherical model, its ground state is superextensive,…

We introduce a representation via (n+1)-colored graphs of compact n-manifolds with (possibly empty) boundary, which appears to be very convenient for computer aided study and tabulation. Our construction is ageneralization to arbitrary…

In S. Giombi, I. Klebanov, F. Popov, S. Prakash and G. Tarnopolsky, {\it Phys. Rev.} {\bf D} 98 (2018) 10, 105005, a prismatic tensor model was introduced. We study here the diagrammatics and the double scaling limit of this model, using…

We present a class of models in which the top quark, by mixing with new physics at a higher energy scale, is naturally heavier than the other standard model particles. We take this new physics to be extended color. Our models contain new…

We give superexponential lower and upper bounds on the number of coloured $d$-dimensional triangulations whose underlying space is an oriented manifold, when the number of simplices goes to infinity and $d\geq 3$ is fixed. In the special…

We review the combinatorial, topological, algebraic and metric properties supported by $(D+1)$-colored graphs, with a focus on those that are pertinent to the study of tensor model theories. We show how to extract a limiting continuum…

The expansion $G^+$ of a graph $G$ is the $3$-uniform hypergraph obtained from $G$ by enlarging each edge of $G$ with a new vertex disjoint from $V(G)$ such that distinct edges are enlarged by distinct vertices. Let $ex_3(n,F)$ denote the…

We compute the structure constants of topological symmetric orbifold theories up to third order in the large N expansion. The leading order structure constants are dominated by topological metric contractions. The first order interactions…