Related papers: Veronese Geometry and the Electroweak Vacuum Modul…
In this paper we provide a systematic treatment of Willmore surfaces with orientation reversing symmetries and illustrate the theory by (old and new) examples. We apply our theory to isotropic Willmore two-spheres in $S^4$ and derive a…
We present a complete classification of the vacuum geometries of all renormalizable superpotentials built from the fields of the electroweak sector of the MSSM. In addition to the Severi and affine Calabi-Yau varieties previously found, new…
For d > 1, we consider the Veronese map of degree d on a complex vector space W , Ver_d : W -> Sym^d W , w -> w^d , and denote its image by Z. We describe the characters of the simple GL(W)-equivariant holonomic D-modules supported on Z. In…
The topological mechanism for generation of vector boson masses in the Electroweak Model is discussed. Vector boson masses are automatically generated by transformation of the free Lagrangian from the noncompact $R_4$ matter fields space to…
We consider a moduli space of lattice polarized K3 surfaces with the additional information of a frame of the trascendental cohomology with respect to the lattice polarization. This moduli space is proved to be quasi-affine, and the…
We analyse symmetry breaking in the Weinberg-Salam model paying particular attention to the underlying geometry of the theory. In this context we find two natural metrics upon the vacuum manifold: an isotropic metric associated with the…
Moduli spaces of hyperbolic surfaces may be endowed with a symplectic structure via the Weil-Petersson form. Mirzakhani proved that Weil-Petersson volumes exhibit polynomial behaviour and that their coefficients store intersection numbers…
This article is concerned with an extensive study of an infinite-dimensional Lie algebra $\mathfrak{sv}$, introduced in the context of non-equilibrium statistical physics, containing as subalgebras both the Lie algebra of invariance of the…
Apart from global topological problems an affine homogeneous space is locally described by its curvature, its torsion and a slightly less tangible object called its connection in a given base point. Using this description of the local…
Motivated by the famous and pioneering mathematical works by Perelman, Hamilton, and Thurston, we introduce the concept of using modern geometrical mathematical classifications of multi-dimensional manifolds to characterize electronic…
We analyze some features of the role that extra dimensions, of radius $R$ in the TeV$^{-1}$ range, can play in the soft breaking of supersymmetry and the spontaneous breaking of electroweak symmetry. We use a minimal model where the gauge…
We show how spontaneous supersymmetry breaking in the vacuum state of higher-derivative supergravity is transmitted, as explicit soft supersymmetry-breaking terms, to the effective Lagrangian of the standard electroweak model. The general…
We investigate a model of dynamical electroweak symmetry breaking via a dual gravitational description. The gravity dual is obtained by embedding a D7 - anti-D7 pair of branes into a type IIB background that is dual to a walking gauge…
We propose an algebraic geometry-inspired approach for constructing entangled subspaces within the Hilbert space of a multipartite quantum system. Specifically, our method employs a modified Veronese embedding, restricted to the conic, to…
We present an intriguing and precise interplay between algebraic geometry and the phenomenology of generations of particles. Using the electroweak sector of the MSSM as a testing ground, we compute the moduli space of vacua as an algebraic…
Segre-Veronese manifolds are smooth submanifolds of tensors comprising the partially symmetric rank-1 tensors. We investigate a one-parameter family of warped geometries of Segre-Veronese manifolds, which includes the standard Euclidean…
Using first-principle lattice simulations, we demonstrate that in the background of a strong magnetic field (around $10^{20}$ T), the electroweak sector of the vacuum experiences two consecutive crossover transitions associated with…
In the present survey we collect some recent results on nuclei of Veronese varieties and invariant subspaces of normal rational curves. We must assume, however, that the ground field is not "too small", since otherwise a Veronese variety is…
In this work we present a useful way to introduce the octonionic projective and hyperbolic plane through the use of Veronese vectors. Then we focus on their relation with the exceptional Jordan algebra and show that the Veronese vectors are…
Lie-type deformations provide a systematic way of generalising the symmetries of modern physics. Deforming the isometry group of Minkowski spacetime through the introduction of a minimal length scale $\ell$ leads to anti de Sitter spacetime…