Related papers: Loop equations for multi-cut matrix models

We compute the complete topological expansion of the formal hermitian two-matrix model. For this, we refine the previously formulated diagrammatic rules for computing the 1/ N expansion of the nonmixed correlation functions and give a new…

We study the problem of hierarchical clustering on planar graphs. We formulate this in terms of an LP relaxation of ultrametric rounding. To solve this LP efficiently we introduce a dual cutting plane scheme that uses minimum cost perfect…

We derive one-point functions of the loop operators of Hermitian matrix-chain models at finite $N$ in terms of differential operators acting on the partition functions. The differential operators are completely determined by recursion…

Multi-cut critical points and their macroscopic loop amplitudes are studied in the multi-cut two-matrix models, based on an extension of the prescription developed by Daul, Kazakov and Kostov. After identifying possible critical points and…

We present a method to compute the genus expansion of the free energy of Hermitian matrix models from the large N expansion of the recurrence coefficients of the associated family of orthogonal polynomials. The method is based on the…

We consider the calculation of the master integrals of the three-loop massive banana graph. In the case of equal internal masses, the graph is reduced to three master integrals which satisfy an irreducible system of three coupled linear…

We present an extension of the duality theorem, previously defined by S. Catani et al. on the one-loop level, to higher loop orders. The duality theorem provides a relation between loop integrals and tree-level phase-space integrals. Here,…

We formulate a notion of abstract loop equations, and show that their solution is provided by a topological recursion under some assumptions, in particular the result takes a universal form. The Schwinger-Dyson equation of the one and two…

We present a method, based on loop equations, to compute recursively all the terms in the large $N$ topological expansion of the free energy for the 2-hermitian matrix model. We illustrate the method by computing the first subleading term,…

We provide analytic results for two-loop four-point master integrals with one massive propagator and one massive leg relevant to single top production. Canonical bases of master integrals are constructed and the Simplified Differential…

We introduce and study the Hermitian matrix model with potential V(x)=x^2/2-stx/(1-tx), which enumerates the number of linear chord diagrams of fixed genus with specified numbers of backbones generated by s and chords generated by t. For…

Recently we showed how, in two-dimensional scalar theories, one-loop threshold diagrams can be cut into the product of one or more tree-level diagrams arXiv:2206.09368. Using this method on the ADE series of Toda models, we computed the…

We present a method for the computation of hepta-cuts of two loop scattering amplitudes. Four dimensional unitarity cuts are used to factorise the integrand onto the product of six tree-level amplitudes evaluated at complex momentum values.…

We review one dimensional matrix theory and its variations, collective field theory and quantum phase space description. In the planar limit, these theories become classical and can be easily analyzed. With these descriptions, one…

This paper provides the constructive loop vertex expansion for stable matrix models with (single trace) interactions of arbitrarily high even order in the Hermitian and real symmetric cases. It relies on a new and simpler method which can…

We define and solve classes of sparse matrix problems that arise in multilevel modeling and data analysis. The classes are indexed by the number of nested units, with two-level problems corresponding to the common situation in which data on…

We present the loop-loop correlation model that allows us to compute confining flux tubes and to examine their effects and manifestations in high-energy reactions.

We investigate the multi-loop correlators and the multi-point functions for all of the scaling operators in unitary minimal conformal models coupled to two-dimensional gravity from the two-matrix model. We show that simple fusion rules for…

Using the multivariate residue calculus of Leray, we give a precise definition of the notion of a cut Feynman integral in dimensional regularization, as a residue evaluated on the variety where some of the propagators are put on shell.…

We briefly review numerical methods for calculations beyond one loop and then describe new developments within the method of sector decomposition in more detail. We also discuss applications to two-loop integrals involving several mass…