Related papers: Duality between Lines and Points

These Notes deal with various areas of mathematics, and seek reciprocal combinations, explore mutual relations, ranging from abstract objects to problems in physics.

Self-duality equations for Yang-Mills fields in d-dimensional Euclidean spaces consist of linear algebraic relations amongst the components of the curvature tensor which imply the Yang-Mills equations. For the extension to superspace gauge…

The fundamental duality theories relating algebra and geometry that were discovered in the mid-20th century can also be applied to logic via its algebraization under categorical logic. They thereby result in known and new completeness…

This work deals with the notion of Newton complementary duality as raised originally in the work of the second author and B. Costa. A conceptual revision of the main steps of the notion is accomplished which then leads to a vast…

Dimension-varying linear systems are investigated. First, a dimension-free state space is proposed. A cross dimensional distance is constructed to glue vectors of different dimensions together to form a cross-dimensional topological space.…

Gauge theories in four dimensions can exhibit interesting low energy phenomena, such as infrared enhancements of global symmetry. We explore a class of 4d N=1 gauge theories arising from a construction that is motivated by duality walls in…

We extend the notion of polar duality to pairs of transverse Lagrangian planes in the standard symplectic space. This allows us to show that polar duality has a natural interpretation in terms of symplectic geometry. We apply our results to…

Although the introduction of generalised and extended geometry has been motivated mainly by the appearance of dualities upon reductions on tori, it has until now been unclear how (all) the duality transformations arise from first principles…

Lorentz covariant generalisations of the notions of supersymmetry, superspace and self-duality are discussed. The essential idea is to extend standard constructions by allowing tangent vectors and coordinates which transform according to…

Linear Geometry studies geometric properties which can be expressed via the notion of a line. All information about lines is encoded in a ternary relation called a line relation. A set endowed with a line relation is called a liner. So,…

Working within the path-integral framework we first establish a duality between the partion functions of two $U(1)$ gauge theories with a theta term in $d=4$ space-time dimensions. Then, after a dimensional reduction to $d=3$ dimensions we…

We construct a continuously differentiable curve in the plane that can be covered by a collection of lines such that every line intersects the curve at a single point and the union of the lines has Hausdorff dimension 1. We show that for…

We describe a general method to determine dualities between supersymmetric 5d gauge theories. The method is based on performing local S-dualities in the geometry associated to the gauge theory. We find that often a duality can be obtained…

We consider a net of *-algebras, locally around any point of observation, equipped with a natural partial order related to the isotony property. Assuming the underlying manifold of the net to be a differentiable, this net shall be…

We study random dynamical systems on the real line, considering each dynamical system together with the one generated by the inverse maps. We show that there is a duality between forward and inverse behaviour for such systems, splitting…

Beyond normal surfaces there are several open questions concerning 2- dimensional spaces. We present some results and conjectures along this line.

We consider some duality relations for models of non-interacting particles hopping on disordered one-dimensional chains. In particular, we discuss symmetries of bulk-driven barrier and trap models, and relations between boundary-driven and…

This talk reviews some mathematical and physical ideas related to the notion of dimension. After a brief historical introduction, various modern constructions from fractal geometry, noncommutative geometry, and theoretical physics are…

Informally, the 'linear representation hypothesis' is the idea that high-level concepts are represented linearly as directions in some representation space. In this paper, we address two closely related questions: What does "linear…

A class of two-dimensional systems of second-order ordinary differential equations is identified in which a system requires fewer Lie point symmetries than required to solve it. The procedure distinguishes among those which are…