Related papers: On matrix geometry
We study the dynamics of quenched fundamental matter in $\mathcal{N}=2^\ast$ supersymmetric large $N$ SU(N) Yang-Mills theory at zero temperature. Our tools for this study are probe D7-branes in the holographically dual $\mathcal{N}=2^\ast$…
Deep generative models learn a mapping from a low dimensional latent space to a high-dimensional data space. Under certain regularity conditions, these models parameterize nonlinear manifolds in the data space. In this paper, we investigate…
Some general properties of the relativistic $p$-dimensional surface imbedded into $D$-dimensional spacetime and its reduction to the sim\-plest case of the quadratic Lagrangian (the linearized model) are considered. The solutions of the…
We present resent results regarding invertible, non-degenerate solutions of the set-theoretic Yang-Baxter and reflection equations. We recall the notion of braces and we present and prove various fundamental properties required for the…
This is a short presentation of some classical results on finite dimensional complex Lie algebras (classification of nilpotent Lie algebras, deformations and perturbations, contractions and rigidity). We present some applications to…
These lecture notes give a pedagogical and (mostly) self-contained review of some basic aspects of the Matrix model of M-theory. The derivations of the model as a regularized supermembrane theory and as the discrete light-cone quantization…
We provide an elementary systematic discussion of single-trace matrix actions and of the group of matrix reparameterization that acts on them. The action of this group yields a generalized notion of gauge invariance which encompasses…
The development of Noncommutative Geometry is creating a reworking and new possibilities in physics. This paper identifies some of the commutation and derivation structures that arise in particle and field interactions and fundamental…
In this paper we consider two different nonlinear $\sigma$-models minimally coupled to Eddington-inspired Born-Infeld gravity. We show that the resultant geometries represent minimal modifications with respect to those found in GR, though…
For matrix analogues of embedded surfaces we define discrete curvatures and Euler characteristics, and a non-commutative Gauss--Bonnet theorem is shown to follow. We derive simple expressions for the discrete Gauss curvature in terms of…
The subject of this PhD thesis is noncommutative geometry - more specifically spectral triples - and how it can be generalized to semi-Riemannian manifolds generally, and Lorentzian manifolds in particular. The first half of this thesis…
In brane world models our universe is considered as a brane imbedded into a higher dimensional space. We discuss the behaviour of geodesics in the Randall-Sundrum background and point out that free massive particles cannot move along the…
Noncommutative geometry has seen remarkable applications for high energy physics, viz. the geometrical interpretation of the Standard Model. The question whether it also allows for supersymmetric theories has so far not been answered in a…
We carefully investigate the modified Einstein's field equation in a four dimensional (3-brane) arbitrary manifold embedded in a five dimensional Non-Riemannian bulk spacetime with a noncompact extra dimension. In this context the…
Each sub-Riemannian geometry with bracket generating distribution enjoys a background structure determined by the distribution itself. At the same time, those geometries with constant sub-Riemannian symbols determine a unique Cartan…
A mechanism for emergent gravity on brane solutions in Yang-Mills matrix models is exhibited. Newtonian gravity and a partial relation between the Einstein tensor and the energy-momentum tensor can arise from the basic matrix model action,…
We emphasize the necessity of a delicate interplay between the gauge and gravitational sectors of five-dimensional brane worlds in creating phenomenologically relevant vacua. We discuss locally supersymmetric brane worlds with unflipped and…
We examine the hypothesis that space-time is a product of a continuous four-dimensional manifold times a finite space. A new tensorial notation is developed to present the various constructs of noncommutative geometry. In particular, this…
We study the embedding of D7 brane probes in five geometries that are deformations of AdS_5 x S^5. Each case corresponds to the inclusion of quark fields in a dual gauge theory where we are interested in investigating whether chiral…
We study geometric properties of the gradient flow for learning deep linear convolutional networks. For linear fully connected networks, it has been shown recently that the corresponding gradient flow on parameter space can be written as a…