Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userLocal model for the moduli space of affine vortices
49
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We show that the moduli space of regular affine vortices, which are solutions of the symplectic vortex equation over the complex plane, has the structure of a smooth manifold. The construction uses Zilteners Fredholm theory results [31]. We also extend the result to the case of affine vortices over the upper half plane. These results are necessary ingredients in defining the open quantum Kirwan map proposed by Woodward [24].
rate research
Read More
We construct a gluing map for stable affine vortices over the upper half plane with the Lagrangian boundary condition at a rigid, regular, codimension one configuration. This construction plays an important role in establishing the relation between the gauged linear sigma model and the nonlinear sigma model in the presence of Lagrangian branes.
The moduli space of flat SU(2) connections on a punctured surface, having prescribed holonomy around the punctures, is a compact smooth manifold if the prescription is generic. This paper gives a direct, elementary proof that the trace of the holonomy around a certain loop determines a Bott-Morse function on the moduli space which is perfect, meaning that the Morse inequalities are equalities. This leads to an attractive recursion for the Betti numbers of the moduli space, which agrees with the Harder-Narasimhan formula in the case of one puncture with holonomy -1.
We consider deformations of torsion-free G2 structures, defined by the G2-invariant 3-form $phi$ and compute the expansion of the Hodge star of $phi$ to fourth order in the deformations of $phi$. By considering M-theory compactified on a G2 manifold, the G2 moduli space is naturally complexified, and we get a Kahler metric on it. Using the expansion of the Hodge star of $phi$ we work out the full curvature of this metric and relate it to the Yukawa coupling.
The dynamics of both global and local vortices with non-Abelian orientational moduli is investigated in detail. Head-on collisions of these vortices are numerically simulated for parallel, anti-parallel and orthogonal internal orientations where we find interesting dynamics of the orientational moduli. A detailed study of the inter-vortex force is provided and a phase diagram separating Abelian and non-Abelian vortex types is constructed. Some results on scatterings with non-zero impact parameter and multi-vortex collisions are included.
In this article we study Weinstein structures endowed with a Lefschetz fibration in terms of the Legendrian front projection. First we provide a systematic recipe for translating from a Weinstein Lefschetz bifibration to a Legendrian handlebody. Then we present several applications of this technique to symplectic topology. This includes the detection of flexibility and rigidity for several families of Weinstein manifolds and the existence of closed exact Lagrangian submanifolds. In addition, we prove that the Koras--Russell cubic is Stein deformation equivalent to affine complex 3-space and verify the affine parts of the algebraic mirrors of two Weinstein 4-manifolds.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
