Related papers: Synopsis of Duality
Double field theory and exceptional field theory are formulations of supergravity that make certain dualities manifest symmetries of the action. To achieve this, the geometry is extended by including dual coordinates corresponding to…
We extend the closed graph theorem and the open mapping theorem to a context in which a natural duality interchanges their extensions.
Properties of the recently reported homogeneous Hilbert curves are deduced and reported. The nature of the affine transformations involved in the construction of the Hilbert curves is explored. The analytical representation of proper and…
The concepts of symmetry and its breakdown are investigated in two different terms according to whether the resulting asymmetry is universal or only obtained for a special configuration: we shall illustrate this by considering in the first…
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…
Duality is an indispensable tool for describing the strong-coupling dynamics of gauge theories. However, its actual realization is often quite subtle: quantities such as the partition function can transform covariantly, with degrees of…
We survey research that studies the connection between the computational complexity of optimization problems on the one hand, and the duality gap between the primal and dual optimization problems on the other. To our knowledge, this is the…
A short note on bounds on distance to variety of a point in terms of the Taylor coefficients at the point.
A flat membrane with given shape is displayed; two points in the membrane are randomly selected; the probability that the separation between the points have a specified value is sought. A simple method to evaluate the probability density is…
The bridge index and superbridge index of a knot are important invariants in knot theory. We define the bridge map of a knot conformation, which is closely related to these two invariants, and interpret it in terms of the tangent indicatrix…
We investigate geometric properties of surfaces given by certain formulae. In particular, we calculate the singular curvature and the limiting normal curvature of such surfaces along the set of singular points consisting of singular points…
This gives some information about the conformal point and the calibrating conic, and their relationship one to the other. These concepts are useful for visualizing image geometry, and lead to intuitive ways to compute geometry, such as…
Recently a duality between color and kinematics has been proposed, exposing a new unexpected structure in gauge theory and gravity scattering amplitudes. Here we propose that the relation goes deeper, allowing us to reorganize amplitudes…
A bisection line divides a convex planar curve into two parts with equal areas. It is natural to study the envelope of these lines, which in general present singularities. The polygonal case is particularly inte\-resting, since there are…
Congruences, or $2$-parameter families of lines in $3$-space are of interest in many situations, in particular in geometric optics. In this paper we consider elements of their geometry which are invariant under affine changes of…
A set of on shell duality equations is proposed that leads to a map between strings moving on symmetric spaces with opposite curvatures. The transformation maps "waves" on a riemannian symmetric space to "waves" on its dual riemannian…
We review the notion of symplectic duality earlier introduced in the context of topological recursion. We show that the transformation of symplectic duality can be expressed as a composition of $x-y$ dualities in a broader context of log…
The duality between the Cartesian coordinates on the Minkowski space-time and the Dirac field is investigated. Two distinct possibilities to define this duality are shown to exist. In both cases, the equations satisfied by prepotentials are…
The concepts of geometric phase and wave-particle duality are interlinked to several fundamental phenomena in quantum physics, but their mutual relationship still forms an uncharted open problem. Here we address this question by studying…
We argue that the T-duality phenomenon is not exclusively a stringy effect but it is relevant also in the context of the standard point particle dynamics. To illustrate the point, we construct a four-parametric family of four-dimensional…