Super Calabi-Yau’s and Special Lagrangians

نویسنده

  • R. Ricci
چکیده

We apply mirror symmetry to the super Calabi-Yau manifold CP and show that the mirror can be recast in a form which depends only on the superdimension and which is reminiscent of a generalized conifold. We discuss its geometrical properties in comparison to the familiar conifold geometry. In the second part of the paper examples of special-Lagrangian submanifolds are constructed for a class of super Calabi-Yau’s. We finally comment on their infinitesimal deformations. November 2005 [email protected]

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

The Calabi Conjecture

In this paper we aim to explore the Geometric aspects of the Calabi Conjecture and highlight the techniques of nonlinear Elliptic PDE theory used by S.T. Yau [SY] in obtaining a solution to the problem. Yau proves the existence of a Geometric structure using differential equations, giving importance to the idea that deep insights into geometry can be obtained by studying solutions of such equat...

متن کامل

Lagrangians , stable bundles and mean curvature flow

We make a conjecture about mean curvature flow of Lagrangian submanifolds of Calabi-Yau manifolds, expanding on that of [Th]. We give new results about the stability condition, and propose a Jordan-Hölder-type decomposition of (special) Lagrangians. The main results are the uniqueness of special Lagrangians in hamiltonian deformation classes of Lagrangians, under mild conditions, and a proof of...

متن کامل

Moment Maps, Monodromy and Mirror Manifolds

Via considerations of symplectic reduction, monodromy, mirror symmetry and Chern-Simons functionals, a conjecture is proposed on the existence of special Lagrangians in the hamiltonian deformation class of a given Lagrangian sub-manifold of a Calabi-Yau manifold. It involves a stability condition for graded Lagrangians, and can be proved for the simple case of T 2 .

متن کامل

(Dis)assembling Special Lagrangians

We explain microscopically why split attractor flows, known to underlie certain stationary BPS solutions of four dimensional N = 2 supergravity, are the relevant data to describe wrapped D-branes in Calabi-Yau compactifcations of type II string theory. We work entirely in the context of the classical geometry of A-branes, i.e. special Lagrangian submanifolds, avoiding both the use of homologica...

متن کامل

ar X iv : m at h / 01 11 11 1 v 2 [ m at h . D G ] 2 5 Ju n 20 02 Lectures on special Lagrangian geometry

Calabi–Yau m-folds (M,J, ω,Ω) are compact complex manifolds (M,J) of complex dimension m, equipped with a Ricci-flat Kähler metric g with Kähler form ω, and a holomorphic (m, 0)-form Ω of constant length |Ω| = 2. Using Algebraic Geometry and Yau’s solution of the Calabi Conjecture, one can construct them in huge numbers. String Theorists (a species of theoretical physicist) are very interested ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2005