摘要翻译:
我们利用多曲面几何研究紧Calabi-Yau流形上的开弦镜像对称性。对于镜面对上的镜面对,我们导出了一个正则超几何微分方程组,它的解决定了球面和圆盘的开/闭弦镜像映射和配分函数。我们定义了一个膜几何的线性sigma模型,并描述了对偶二重多面体和二重膜几何之间的对应关系。应用该方法研究了变形空间中不同点的膜模量有阻塞和经典无阻塞的例子。在开/闭变形空间上,计算平面坐标下的大体积瞬子展开式,得到了枚举不变量的预测。
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英文标题:
《Mirror Symmetry for Toric Branes on Compact Hypersurfaces》
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作者:
M. Alim, M. Hecht, P. Mayr, A. Mertens
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最新提交年份:
2009
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分类信息:
一级分类:Physics 物理学
二级分类:High Energy Physics - Theory 高能物理-理论
分类描述:Formal aspects of quantum field theory. String theory, supersymmetry and supergravity.
量子场论的形式方面。弦理论,超对称性和超引力。
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一级分类:Mathematics 数学
二级分类:Algebraic Geometry 代数几何
分类描述:Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇,叠,束,格式,模空间,复几何,量子上同调
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英文摘要:
We use toric geometry to study open string mirror symmetry on compact Calabi-Yau manifolds. For a mirror pair of toric branes on a mirror pair of toric hypersurfaces we derive a canonical hypergeometric system of differential equations, whose solutions determine the open/closed string mirror maps and the partition functions for spheres and discs. We define a linear sigma model for the brane geometry and describe a correspondence between dual toric polyhedra and toric brane geometries. The method is applied to study examples with obstructed and classically unobstructed brane moduli at various points in the deformation space. Computing the instanton expansion at large volume in the flat coordinates on the open/closed deformation space we obtain predictions for enumerative invariants.
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PDF链接:
https://arxiv.org/pdf/0901.2937