Related papers: Opposite relation on dual polar spaces and half-sp…
In this article we use the cluster structure on the Grassmannian and the combinatorics of plabic graphs to exhibit a new aspect of mirror symmetry for Grassmannians in terms of polytopes. For our $A$-model, we consider the Grassmannian…
The coupling of gravity to a scalar field raises a number of interesting questions of principle since the usual minimal coupling obtained by replacing ordinary derivatives with covariant derivatives is not available -- they are the same…
Semiclassical expansion of the Wigner function for spin-1/2 fermions having an effective spacetime-dependent mass is used to analyze spin-polarization effects. The existing framework is reformulated to obtain a differential equation…
Given a five dimensional space endowed with a Cartan distribution, the abnormal geodesics form another five dimensional space with a cone structure. Then it is shown, if the cone structure is regarded as a control system, then, the space of…
Riemannian and Absolute Parallelism (AP) geometries are discussed. A lavish treatment of path equations in the AP-space using the Bazanski-type Lagrangian is presented; We write down an expression that is absolutely conserved along a curve…
In a previous paper we showed that for every polarization on an abelian variety there is a dual polarization on the dual abelian variety. In this note we extend this notion of duality to families of polarized abelian varieties. As a main…
Totally symmetric arbitrary spin conformal fields in (A)dS space of even dimension greater than or equal to four are studied. Ordinary-derivative and gauge invariant Lagrangian formulation for such fields is obtained. Gauge symmetries are…
Gravitational interactions are treated as non-associative part of a Lagrangian of octonion fields. The Lagrangian is defined in the charge space as squared curvature with respect to the octonion fields. The applications of suggested…
From a deformed AdS$_5$ space, we used the string/gauge duality to study the deep inelastic scattering for unpolarized fermions with spin 1/2, considering the large Bjorken $x$ parameter regime. Here, we also took into account an anomalous…
We review recent work on holographic aspects of electric-magnetic dualities in theories that involve conformally coupled scalars and abelian gauge fields in asymptotically AdS4 spaces. Such models are relevant for the holographic…
We generalize the electromagnetic duality between a massless, canonical scalar field and a 2-form gauge field in 4-dimensional spacetime to scalar-tensor theories. We derive the action of 2-form gauge field that is dual to two kinds of…
In this paper we study the behaviour of the holomorphic sectional curvature (or Gaussian curvature) of the Bergman metric of planar annuli. The results are then utilized to construct a domain for which the curvature is divergent at one of…
We argue that a necessary condition for hypoellipticity is that the polar is not a spiral domain.
A dual pair formulation for asymmetric locally convex spaces is developed that strictly generalises the ordinary vector space setting. The concept of a polar topology carries over to the asymmetric case and some familiar results are…
Lie derivatives of various geometrical and physical quantities define symmetries and conformal symmetries in general relativity. Thus we obtain motions, collineations, conformal motions and conformal collineations. These symmetries are used…
We consider a special correlation function in the isotropic spin-$\half$ Heisenberg antiferromagnet. It is the probability of finding a ferromagnetic string of (adjacent) spins in the antiferromagnetic ground state. We give two different…
In symmetric spaces of rank one we obtain a right inverse of the Cartan differential on exact differential forms as an integral operator. As a corollary we extend Gauss linking integral beyond space forms.
We describe for any Riemannian manifold a certain infinitesimal neighbourhood of the diagonal. Semi-conformal maps are analyzed as those that preserve such neighbourhoods; harmonic maps are analyzed as those that preserve mirror image…
Positivity restrains the allowed domains for pairs or triples of spin observables in polarised reactions. Various domain shapes in ${1\over2}+{1\over2}\to{1\over2}+{1\over2}$ reactions are displayed. Some methods to determine these domains…
Localization methods have produced explicit expressions for the sphere partition functions of (2,2) superconformal field theories. The mirror symmetry conjecture predicts an IR duality between pairs of Abelian gauged linear sigma models, a…