Related papers: The Geometry of Self-dual 2-forms

We consider the four dimensional scale invariant N=2 SU quiver gauge theories with USp(2N) ends or SU(2N) ends with antisymmetric matter representations. We argue that these theories are realized as six dimensional A_{2N-1} (0,2) theories…

We give a topological characterization of the n-dimensional pseudo-boundary of the (2n+1)-dimensional Euclidean space.

Motivated by a question from V. Arnold about self-dual curves in projective spaces, we study {\cal M}_{m,n,k}: the moduli space of m-self-dual n-gons in {\mathbb P}^k. This paper lays out an explicit construction of self-dual polygons, and…

We consider varieties of representations and characters of 2 and 3-dimensional orbifolds in semisimple Lie groups, and we focus on computing their dimension. For hyperbolic 3-orbifolds, we consider the component of the variety of characters…

The properties of Dirac gamma matrices in a four-dimensional space-time with the $(2,2)$ signature are studied. The basic spinors are classified, and the existence of Majorana-Weyl spinors is noted. Supersymmetry in $2 + 2$ dimensions is…

We describe relations between hyperbolic geometry and codimension two knots or, more exactly, between varieties of conjugacy classes of discrete faithful representations of the fundamental groups of hyperbolic n-manifolds M into…

An alternative to the representation of complex relativity by self-dual complex 2-forms on the spacetime manifold is presented by assuming that that the bundle of real 2-forms is given an almost-complex structure. From this, one can define…

This is the second of two papers that describe a compactness theorem for sequences of solutions of certain SL(2;C) analogs of the anti-self dual equations on oriented, 4-dimensional Riemannian manifolds. This paper proves theorems that…

Let K be a (commutative) field with characteristic not 2, and V be a linear subspace of n by n matrices that have at most two eigenvalues in K (respectively, at most one non-zero eigenvalue in K). We prove that the dimension of V is less…

We formulate the uniformisation problem underlying the geometry of W_n-gravity using the differential equation approach to W-algebras. We construct W_n-space (analogous to superspace in supersymmetry) as an (n-1) dimensional complex…

We find the characterization of maximum dimensional proper-biharmonic integral $\mathcal{C}$-parallel submanifolds of a Sasakian space form and then classify such submanifolds in a 7-dimensional Sasakian space form. Working in the sphere…

This paper develops a construction of families of $ U(1)^{n-2} $-invariant special Lagrangian $ n $-folds in $ \mathbb{C}^{n} $, extending the analytic framework introduced by Joyce ($ n = 3 $) to arbitrary dimension. By reducing the…

We consider the dual space of linear groups over Dynkinian and Euclidean algebras, i.e. finite dimensional algebras derived equivalent to the path algebra of Dynkin or Euclidean quiver. We prove that this space contains an open dense subset…

Given a compact $n$-dimensional immersed Riemannian manifold $M^n$ in some Euclidean space we prove that if the Hausdorff dimension of the singular set of the Gauss map is small, then $M^n$ is homeomorphic to the sphere $S^n$. Also, we…

This paper explores the geometry of the space of codimension-2 submanifolds. We implicitly represent these submanifolds by a class of complex-valued functions. We show that the space of all these implicit representations admits a prequantum…

This paper deals with some basic constructions of linear and multilinear algebra on finite-dimensional diffeological vector spaces. We consider the diffeological dual formally checking that the assignment to each space of its dual defines a…

The superselection sectors of two classes of scalar bilocal quantum fields in D>=4 dimensions are explicitly determined by working out the constraints imposed by unitarity. The resulting classification in terms of the dual of the respective…

An overview of matter-coupled ${\cal N}=2$ supergravity theories with 8 real supercharges, in 4,5 and 6 dimensions is given. The construction of the theories by superconformal methods is explained from basic principles. Special geometry is…

Two-dimensional N=1,2 supersymmetric chiral models and their dual extensions are introduced and canonically quantized. Working within a superspace formalism, the non-manifest invariance under 2D-superPoincare' transformations is proven. The…

We prove that an alternating e-form on a vector space over a quasi-algebraically closed field always has a singular (e-1)-dimensional subspace, provided that the dimension of the space is strictly greater than e. Here an (e-1)-dimensional…