Related papers: Symplectic Structures and Self -dual Fields in (4k…
The `electromagnetic' $Sl(2;\bZ)$ duality group in spacetime dimension $D=4k$ can be given a Kaluza-Klein interpretation in $D=4k+2$ as the modular group of a compactifying torus. We show how dyonic $2(k-1)$-branes in $D=4k$ can be…
We use explicit pseudoholomorphic curve techniques (without virtual perturbations) to define a sequence of symplectic capacities analogous to those defined recently by the second named author using symplectic field theory. We then compute…
This paper studies novel four-dimensional integrable field theories that are deformations of self-dual Yang-Mills. They are engineered by considering holomorphic Chern-Simons and BF type theories on covers of twistor space obtained by…
A Siegel-type chiral p-form action is proposed in D=2(p+1) spacetime dimensions. The approach we adopt is to realize the symmetric second-rank Lagrange-multiplier field, introduced in Siegel's action, in terms of a normalized multiplication…
We give a method to lift $(2,0)$-tensors fields on a manifold $M$ to build symplectic forms on $TM$. Conversely, we show that any symplectic form $\Om$ on $TM$ is symplectomorphic, in a neighborhood of the zero section, to a symplectic form…
In this paper we study symplectic involutions and quadratic pairs that become hyperbolic over the function field of a conic. In particular, we classify them in degree 4 and deduce results on 5 dimensional minimal quadratic forms, thus…
In this paper we develop some combinatorial models for continuous spaces. In this spirit we study the approximations of continuous spaces by graphs, molecular spaces and coordinate matrices. We define the dimension on a discrete space by…
In this paper, we construct singular Lagrangian fibrations on some examples of disk cotangent bundles in dimensions 4 and 6. As an application, we show how this construction can be used to obtain toric domains in some cases. In particular,…
We show that the Poisson structure on the smooth locus of a moduli space of 1-dimensional sheaves on a Poisson projective surface $X$ over $\mathbb C$ is a reduction of a natural symplectic structure.
We discuss the structure of heterotic/type II duality in four dimensions as a consequence of string-string duality in six dimensions. We emphasize the new features in four dimensions which go beyond the six dimensional vacuum structure and…
Some aspects of the connection between differential geometry and multidimensional soliton equations are discussed.
Instantons, monopoles and vortices have become paradigms of topological structures in field theory and quantum mechanics, with important applications in particle physics, astrophysics, condensed matter physics and mathematics. We have…
It is conjectured that the symplectic structure of space-time is superior to the metric one. Instead of the commonly adopted pseudo-orthogonal groups SO(1,d-1), d\ge4, the complex symplectic ones Sp(2l,C), l\ge1 are proposed as the local…
We investigate features of duality in three dimensional N=2 Chern-Simons matter theories conjectured to describe M2 branes at toric Calabi Yau four-fold singularities. For 3D theories with non-chiral 4D parents we propone a Seiberg-like…
We discuss the precise relation of the open N=2 string to a self-dual Yang-Mills (SDYM) system in 2+2 dimensions. In particular, we review the description of the string target space action in terms of SDYM in a ``picture hyperspace''…
The fractal structure of directed percolation clusters, grown at the percolation threshold inside parabolic-like systems, is studied in two dimensions via Monte Carlo simulations. With a free surface at y=\pm Cx^k and a dynamical exponent…
We establish an existence $h$-principle for symplectic cobordisms of dimension $2n>4$ with concave overtwisted contact boundary.
We review some examples of heterotic/type II string duality which shed light on the infrared dynamics of string compactifications with N=2 and N=1 supersymmetry in four dimensions.
In this article, we introduce symplectic reduction in the framework of nonrational toric geometry. When we specialize to the rational case, we get symplectic reduction for the action of a general, not necessarily closed, Lie subgroup of the…
The dual of the four dimensional non-linear sigma model is constructed using techniques familiar to string theory. This construction necessitates the introduction of a rank two antisymmetric tensor field whose properties are examined. The…