arXiv 2104.027182021-04hep-th

单参数Calabi-Yau流形族的大复结构吸引子

Attractors with Large Complex Structure for One-Parameter Families of Calabi-Yau Manifolds

Philip Candelas, Pyry Kuusela, Joseph McGovern

备注：: v2: typos corrected, references added
DOI：: 10.1007/JHEP11(2021)032

摘要：

在大的复杂结构区域内研究了任意单参数Calabi-Yau流形族的吸引子方程。这些方程被迭代求解，产生我们称之为N-展开的东西，它是流形的Gromov-Witten不变量中的幂级数。该级数的系数与整数分区相关联。在重要的情况下，我们能够找到这种展开式的一般项的封闭形式的表达式。据我们所知，这些是第一个通用的解决方案，吸引子方程，纳入瞬子的贡献。特别是，我们发现一个简单的封闭形式的熵公式相关联的排名两个吸引点，包括最近发现的。我们的解决方案的应用进行了简要讨论。最重要的是，我们能够给出一个表达式的Wald熵的黑洞，包括所有的属0瞬子修正。

英文摘要：

The attractor equations for an arbitrary one-parameter family of Calabi-Yau manifolds are studied in the large complex structure region. These equations are solved iteratively, generating what we term an N-expansion, which is a power series in the Gromov-Witten invariants of the manifold. The coefficients of this series are associated with integer partitions. In important cases we are able to find closed-form expressions for the general term of this expansion. To our knowledge, these are the first generic solutions to attractor equations that incorporate instanton contributions. In particular, we find a simple closed-form formula for the entropy associated to rank two attractor points, including those recently discovered. The applications of our solutions are briefly discussed. Most importantly, we are able to give an expression for the Wald entropy of black holes that includes all genus 0 instanton corrections.

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英文摘要：

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