Related papers: The $n$-point Exceptional Universe

We present the first example of a grand unified theory (GUT) with a modular symmetry interpreted as a family symmetry. The theory is based on supersymmetric $SU(5)$ in 6d, where the two extra dimensions are compactified on a…

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…

We obtain a generic regularity result for stationary integral $n$-varifolds with only strongly isolated singularities inside $N$-dimensional Riemannian manifolds, in absence of any restriction on the dimension ($n\geq 2$) and codimension.…

We discuss real-space lattice models equivalent to gauge theories with a discrete non-Abelian gauge group. We construct the Hamiltonian formalism which is appropriate for their solid-state physics implementation and outline their basic…

We compute tree-level $n$-point scattering amplitudes in scalar field theories in terms of geometric invariants on a fibre bundle. All 0- and 2-derivative interactions are incorporated into a metric on this bundle. The on-shell amplitudes…

In the context of six-dimensional supergravity there is a special class of parent models for five-dimensional theories defined by the four Euclidean simple Jordan algebras of degree 3. We extend this result to include six- dimensional…

Special generic maps are generalizations of Morse functions with exactly two singular points on spheres and canonical projections of unit spheres. They restrict the manifolds of the domains strongly in considerable cases and are important…

In this paper, we classify four-dimensional Jordan algebras over an algebraically closed field of characteristic different of two. We establish the list of 73 non-isomorphic Jordan algebras.

In this article we study the interplay between algebro-geometric notions related to $\pi$-points and structural features of the stable Auslander-Reiten quiver of a finite group scheme. We show that $\pi$-points give rise to a number of new…

We classify maximal totally geodesic submanifolds in exceptional symmetric spaces up to isometry. Moreover, we introduce an invariant for certain totally geodesic embeddings of semisimple symmetric spaces, which we call the Dynkin index. We…

We investigate $N$-extended supersymmetry in one-dimensional quantum mechanics on a circle with point singularities. For any integer $n$, $N=2n+1$ supercharges are explicitly constructed in terms of discrete transformations, and a class of…

Jordan algebras arise naturally in (quantum) information geometry, and we want to understand their role and their structure within that framework. Inspired by Kirillov's discussion of the symplectic structure on coadjoint orbits, we provide…

In this work we review a systematic, algorithmic construction of dual heterotic/F-theory geometries corresponding to 4-dimensional, N = 1 supersymmetric compactifications. We look in detail at a class of well-defined Calabi-Yau fourfolds…

We consider semidifferentiable (possibly nonsmooth) maps, acting on a subset of a Banach space, that are nonexpansive either in the norm of the space or in the Hilbert's or Thompson's metric inherited from a convex cone. We show that the…

We study exceptional Jordan algebras and related exceptional group schemes over commutative rings from a geometric point of view, using appropriate torsors to parametrize and explain classical and new constructions, and proving that over…

Using spinorial geometry techniques, we classify the supersymmetric solutions of euclidean ${\cal N}=4$ super Yang-Mills theory. These backgrounds represent generalizations of instantons with nontrivial scalar fields turned on, and satisfy…

We reformulate superalgebra and supergeometry in completely categorical terms by a consequent use of the functor of points. The increased abstraction of this approach is rewarded by a number of great advantages. First, we show that one can…

Special generic maps are higher dimensional versions of Morse functions with exactly two singular points, characterizing spheres topologically except 4-dimensional cases and 4-dimensional standard spheres. The class of such maps also…

In this work, we study the geodesic structure for a geometry described by a spherically symmetric four-dimensional solution embedded in a five-dimensional space known as a brane-based spherically symmetric solution. Mainly, we have found…

Exceptional points are complex-valued spectral singularities that lead to a host of intriguing features such as loss-induced transparency - a counterintuitive process in which an increase in the system's overall loss can lead to enhanced…