arXiv 2408.092552024-08hep-th

紧致Calabi-Yau流形上源于M理论的非微扰拓扑弦理论

Non-perturbative topological string theory on compact Calabi-Yau manifolds from M-theory

Jarod Hattab, Eran Palti

备注：: 5 pages, 1 figure. v2: Added references, minor corrections, and an assumption of restriction to smooth and rigid cycles

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AI总结：

本文证明在紧致或非紧致Calabi-Yau三流形上，通过修正M2态目标空间积分计算中的极点问题，可得到完整的非微扰拓扑弦自由能的精确表述。

摘要：

我们证明了在全纯极限下，完整的非微扰拓扑弦自由能仅源于M2态的目标空间积分计算。定性上，这与Gopakumar和Vafa的计算相同，但我们发现由于非微扰物理诱导的极点微妙性，最终表达式必须进行修改。考虑这一修改后得到了类似Gopakumar-Vafa的公式，我们提出将其作为积分过程的精确表述。计算该公式必然需要在复化Schwinger原时参数中进行围道积分。我们证明该计算可得出完整的非微扰拓扑弦自由能，且适用于紧致或非紧致Calabi-Yau三流形。所给出的显式公式在膜包裹的二维圈为刚性且平滑时成立，但该方法论也可用于研究更一般的Calabi-Yau几何。

英文摘要：

We show that the full non-perturbative topological string free energy, in the holomorphic limit, follows simply from a target space integrating out calculation of M2 states. Qualitatively, this is the same as the calculation performed by Gopakumar and Vafa, but we find that the final expression must be modified due to a subtlety with poles induced by non-perturbative physics. Accounting for this modification leads to a Gopakumar-Vafa-like formula, which we propose as the exact formulation of the integrating out procedure. Evaluating the formula necessarily requires a contour integral in a complexified Schwinger proper time parameter. We show that this evaluation yields the full non-perturbative topological string free energy, and can be applied to a compact, or non-compact, Calabi-Yau threefold. The explicit formula presented holds as long as the two-cycles wrapped by the branes are rigid and smooth, but the methodology can be used to study also more general Calabi-Yau geometries.

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