Topological String Theory on Compact Calabi–Yau: Modularity and Boundary Conditions
Topological String Theory on Compact Calabi–Yau: Modularity and Boundary Conditions
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DOI：
10.1007/978-3-540-68030-7_3
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发表时间：
2006-12
期刊：
影响因子：
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通讯作者：
Min-xin Huang;A. Klemm;S. Quackenbush
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文献类型：
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作者：
Min-xin Huang;A. Klemm;S. Quackenbush
在紧Calabi-Yau M上计算了拓扑弦配分函数Z（λ，t，t）=exp（λ 2g-2Fg（t，t））. Fg（t，t）满足全纯反常方程，这意味着Fg =Z在辛空间H3（M，Z）上变换为波函数.这在模空间M（M）中沿着具有优选局部坐标的任何地方定义它。截面Fg的模性质以及来自4d有效作用的局部约束允许我们在很大程度上固定Z。目前，在圆锥形处新发现的间隙条件，在orbifold处的规则性和来自Castelnuovo理论的最幼稚的界限，我们可以提供边界数据，其指定Z，例如，对于五次曲线高达亏格51。
The topological string partition function Z(λ,t,t) =exp(λ2 g-2 Fg(t, t)) is calculated on a compact Calabi–Yau M. The Fg(t, t) fulfil the holomorphic anomaly equations, which imply that ψ=Z transforms as a wave function on the symplectic space H3(M, Z). This defines it everywhere in the moduli space M(M) along with preferred local coordinates. Modular properties of the sections Fg as well as local constraints from the 4d effective action allow us to fix Z to a large extent. Currently with a newly found gap condition at the conifold, regularity at the orbifold and the most naive bounds from Castelnuovo’s theory, we can provide the boundary data, which specify Z, e.g. up to genus 51 for the quintic.