Related papers: Multi-matrix models and emergent geometry
Matrix configurations coming from matrix models comprise many important aspects of modern physics. They represent special quantum spaces and are thus strongly related to noncommutative geometry. In order to establish a semiclassical limit…
We introduce a new class of models for emergent dynamics. It is based on a new communication protocol which incorporates two main features: short-range kernels which restrict the communication to local geometric balls, and anisotropic…
We study the local geometry of empirical risks in high dimensions via the spectral theory of their Hessian and information matrices. We focus on settings where the data, $(Y_\ell)_{\ell =1}^n \in \mathbb{R}^d$, are i.i.d. draws of a…
We consider a reduced model of four-dimensional Yang-Mills theory with a mass term. This matrix model has two classical solutions, two-dimensional fuzzy sphere and two-dimensional fuzzy torus. These classical solutions are constructed by…
We construct F-theory GUT models without exotic matter, leading to the MSSM matter spectrum with potential singlet extensions. The interplay of engineering explicit geometric setups, absence of four-dimensional anomalies, and realistic…
Many complex structures and stochastic patterns emerge from simple kinetic rules and local interactions, and are governed by scale invariance properties in combination with effects of the global geometry. We consider systems that can be…
Nonlinear waves in defocusing media are investigated in the framework of the hydrodynamic description of light as a photon fluid. The observations are interpreted in terms of an emergent curved spacetime generated by the waves themselves,…
We study the phenomenological consequences of higher symmetry structures in axion effective field theories. Higher-group and non-invertible symmetries impose parametric constraints on the energy scales at which different symmetries can…
The phenomena of emergent fuzzy geometry and noncommutative gauge theory from Yang-Mills matrix models is briefly reviewed. In particular, the eigenvalues distributions of Yang-Mills matrix models in lower dimensions in the commuting…
In condensed matter physics gauge symmetries other than the U(1) of electromagnetism are of an emergent nature. Two emergence mechanisms for gauge symmetry are well established: the way these arise in Kramers-Wannier type local-global…
The temporal response of open systems is marked by damped oscillations. These oscillations, often referred to as ringings, are the signature of the decay of quasinormal modes (QNMs). A major research objective across various fields is to…
We search for weakly interacting fixed points in extensions of the minimally supersymmetric standard model (MSSM). Necessary conditions lead to three distinct classes of anomaly-free extensions involving either new quark singlets, new quark…
We prove that many aspects of the differential geometry of embedded Riemannian manifolds can be formulated in terms of multi linear algebraic structures on the space of smooth functions. In particular, we find algebraic expressions for…
Globally coupled doubling maps are studied in this paper. In this setting and for finitely many sites, two distinct bifurcation values of the coupling strength have been identified in the literature, corresponding to the emergence of…
Many systems involve numerous interacting parts and the whole system can have properties that the individual parts do not. I take this novelty as the defining characteristic of an emergent property. Other characteristics associated with…
These notes provide an introduction to the noncommutative matrix geometry which arises within matrix models of Yang-Mills type. Starting from basic examples of compact fuzzy spaces, a general notion of embedded noncommutative spaces…
We consider numerical solution of elliptic problems with heterogeneous diffusion coefficients containing thin highly conductive structures. Such problems arise e.g. in fractured porous media, reinforced materials, and electric circuits. The…
The paper presents a general theory of coupling of eigenvalues of complex matrices of arbitrary dimension depending on real parameters. The cases of weak and strong coupling are distinguished and their geometric interpretation in two and…
In this paper, we focus on statistical region-based active contour models where image features (e.g. intensity) are random variables whose distribution belongs to some parametric family (e.g. exponential) rather than confining ourselves to…
We address a detailed non-perturbative numerical study of the scalar theory on the fuzzy sphere. We use a novel algorithm which strongly reduces the correlation problems in the matrix update process, and allows the investigation of…