Related papers: Solution of all quartic matrix models

This article establishes the existence and multiplicity of normalized solutions to the weighted nonlinear Schr\"odinger-type equation governed by the Caffarelli-Kohn-Nirenberg operator, $$ -\text{div}(|x|^{-2a}\nabla u)=\lambda…

We study the domain of validity of a Schwinger-Dyson (SD) approach to non-equilibrium dynamics when there is broken symmetry. We perform exact numerical simulations of the one- and two-point functions of lambda phi^4 field theory in 1+1…

We choose a complete set of square integrable functions as basis for the expansion of the wavefunction in configuration space such that the matrix representation of the nonrelativistic time-independent wave operator is tridiagonal and…

Let $\lambda_{\phi}(n)$ be the Fourier coefficients of a Hecke holomorphic or Hecke--Maass cusp form on ${\rm SL}_2(\mathbb Z)$, and $f$ be any multiplicative function that satisfies two mild hypotheses. We establish a non-trivial upper…

We confirm by explicit computation the conjectured all-orders iteration of planar maximally supersymmetric N=4 Yang-Mills theory in the nontrivial case of five-point two-loop amplitudes. We compute the required unitarity cuts of the…

We analyze $(2+1)$-dimensional vector-vector type four-Fermi interaction (Thirring) model in the framework of the $1/N$ expansion. By solving the Dyson-Schwinger equation in the large-$N$ limit, we show that in the two-component formalism…

A long standing question in the theory of orthogonal matrix polynomials is the matrix Bochner problem, the classification of $N \times N$ weight matrices $W(x)$ whose associated orthogonal polynomials are eigenfunctions of a second order…

We study the spectrum of SU(2) x SO(2) matrix supersymmetric quantum mechanics. We use angular coordinates that allow us to find an explicit solution of the Gauss law constraints and single out the quantum number n (the Lorentz angular…

We show that for any positive integer $d$, there are families of switched linear systems---in fixed dimension and defined by two matrices only---that are stable under arbitrary switching but do not admit (i) a polynomial Lyapunov function…

We study the solution of minimax problems $\min_x \max_y G(x) + \langle K(x),y\rangle - F^*(y)$ in finite-dimensional Hilbert spaces. The functionals $G$ and $F^*$ we assume to be convex, but the operator $K$ we allow to be non-linear. We…

It is shown that the infinite dimensional critical surface of general euclidean lattice actions in a generic four-dimensional scalar field theory with $\Phi^4$ interactions has a domain of special multicritical points where higher…

In this article, we examine two double-phase variable exponent problems, each formulated within a distinct framework. The first problem is non-variational, as the nonlinear term may depend on the gradient of the solution. The first main…

We derive parametric integral representations for the general $n$-point function of scalar operators in momentum-space conformal field theory. Recently, this was shown to be expressible as a generalised Feynman integral with the topology of…

We consider a scalar Euclidean QFT with interaction given by a bounded, measurable function $V$ such that $V^{\pm}:=\lim_{w\to \pm\infty}V(w)$ exist. We find a field renormalization such that all the $n$-point connected Schwinger functions…

We prove existence of small amplitude, $2\pi \slash \om$-periodic in time solutions of completely resonant nonlinear wave equations with Dirichlet boundary conditions, for any frequency $ \om $ belonging to a Cantor-like set of positive…

We study the two-matrix model for double-scaled SYK model, called ETH matrix model introduced by Jafferis et al [arXiv:2209.02131]. If we set the parameters $q_A,q_B$ of this model to zero, the potential of this two-matrix model is given by…

Considering the question: how non-linear may a non-linear operator be in order to extend the linear regularization theory, we introduce the class of dilinear mappings, which covers linear, bilinear, and quadratic operators between Banach…

We study the consistency of four-point functions of half-BPS chiral primary operators of weight p in four-dimensional N=4 superconformal field theories. The resulting conformal bootstrap equations impose non-trivial bounds for the scaling…

The paper establishes conditions under which there are exact linear representations of nonlinear partial differential equations (Cauchy problems). By introducing a certain linear operator $A$, it is shown that under these conditions there…

This paper is devoted to the existence of positive solutions for a problem related to a fourth-order differential equation involving a nonlinear term depending on a second order differential operator, $$(-\Delta)^2 u=\lambda u+…