以色列内盖夫本-古里安大学Eran Palti团队研究了基于M理论的紧致Calabi-You流形上的非微扰拓扑弦理论。这一研究成果发表在2025年4月1日出版的《高能物理杂志》上。

研究组证明了在全纯极限下，完全非微扰拓扑串自由能简单地从M2态的积分计算中得出。从定性上讲，这与Gopakumar和Vafa进行的计算相同，但他们发现，由于非微扰物理学引起的极点的微妙性，最终表达式必须进行修改。考虑到这一修改，研究组提出了一个类似Gopakumar-Vafa的公式，作为整合程序的精确公式。

计算公式必然需要在复杂的Schwinger适当时间参数中进行轮廓积分。研究组证明，这种评估产生了完整的非微扰拓扑弦自由能，并且可以应用于紧致或非紧致的Calabi-You三重。只要被膜包裹的两个循环是刚性和光滑的，所提出的显式公式就成立，但该方法也可用于研究更一般的Calabi-You几何。

附：英文原文

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

Author: Hattab, Jarod, Palti, Eran

Issue&Volume: 2025-04-01

Abstract: 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.

DOI: 10.1007/JHEP04(2025)017

Source: https://link.springer.com/article/10.1007/JHEP04(2025)017