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arXiv 2102.07776hep-thmath-phmath.AGmath.MP
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内禀非微扰拓扑弦

Intrinsic non-perturbative topological strings

Murad Alim

摘要:

本文研究了模空间中任意族的Calabi-Yau流形上的差分方程,这些差分方程是由拓扑弦论在变形和分解的锥几何上的渐近展开以及拓扑弦论在有限距离的一般奇点附近的渐近展开得到的.在拓扑弦耦合下,得到了这些方程的解析解,这些解由已知的特殊函数给出,可用于提取强耦合展开式和非微扰内容。强耦合展开式显示了D-膜和NS 5-膜贡献的特征,这在五次Calabi-Yau中得到了三重说明。对于解决conifold,一个表达式,涉及Gopakumar-Vafa recrimation以及细化拓扑弦的Nekrasov-Shatashvili极限,并在文献中的预期结果相比。进一步给出了拓扑弦的非微扰配分函数与非交换Donaldson-Thomas不变量的生成函数之间的精确关系。此外,还研究了拓扑弦在分解锥上的奇异小体积轨迹附近的展开。给出并证明了该展开式中主要奇异项和正则项的精确表达式。这个展开的常数项原来是已知的Gromov-Witten常数映射贡献。

英文摘要:

We study difference equations which are obtained from the asymptotic expansion of topological string theory on the deformed and the resolved conifold geometries as well as for topological string theory on arbitrary families of Calabi-Yau manifolds near generic singularities at finite distance in the moduli space. Analytic solutions in the topological string coupling to these equations are found. The solutions are given by known special functions and can be used to extract the strong coupling expansion as well as the non-perturbative content. The strong coupling expansions show the characteristics of D-brane and NS5-brane contributions, this is illustrated for the quintic Calabi-Yau threefold. For the resolved conifold, an expression involving both the Gopakumar-Vafa resummation as well as the refined topological string in the Nekrasov-Shatashvili limit is obtained and compared to expected results in the literature. Furthermore, a precise relation between the non-perturbative partition function of topological strings and the generating function of non-commutative Donaldson-Thomas invariants is given. Moreover, the expansion of the topological string on the resolved conifold near its singular small volume locus is studied. Exact expressions for the leading singular term as well as the regular terms in this expansion are provided and proved. The constant term of this expansion turns out to be the known Gromov-Witten constant map contribution.

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