K_2$ 和量子曲线

IF 1 4区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL Advances in Theoretical and Mathematical Physics Pub Date : 2024-08-14 DOI:10.4310/atmp.2023.v27.n8.a1
Charles F. Doran, Matt Kerr, Soumya Sinha Babu
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引用次数: 0

摘要

Codesido-Grassi-Mariño 2015 年在拓扑弦理论中提出的一个猜想将环状 CY 3$ 折叠的枚举不变式与其镜像曲线上的算子谱联系起来。我们为这些曲线上的 $K_2$ 类积分调节器推导出了这个猜想的两个后果,然后证明了这两个后果;这些结果从而为 CGM 猜想提供了证据。(虽然猜想和推导过程都包含局部镜像对称的形式,但结果/定理却不包含:它们只涉及曲线本身)。我们的第一个定理将高次正函数的零点与一属曲线的算子谱联系起来,并提出了分析与算术几何之间的新联系。第二个定理提供了曲线模中最大圆锥点的调节器周期极限的稀对数公式。
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$K_2$ and quantum curves
A 2015 conjecture of Codesido-Grassi-Mariño in topological string theory relates the enumerative invariants of toric CY $3$-folds to the spectra of operators attached to their mirror curves. We deduce two consequences of this conjecture for the integral regulators of $K_2$-classes on these curves, and then prove both of them; the results thus give evidence for the CGM conjecture. (While the conjecture and the deduction process both entail forms of local mirror symmetry, the consequences/theorems do not: they only involve the curves themselves.) Our first theorem relates zeroes of the higher normal function to the spectra of the operators for curves of genus one, and suggests a new link between analysis and arithmetic geometry. The second theorem provides dilogarithm formulas for limits of regulator periods at the maximal conifold point in moduli of the curves.
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来源期刊
Advances in Theoretical and Mathematical Physics
Advances in Theoretical and Mathematical Physics 物理-物理:粒子与场物理
CiteScore
2.20
自引率
6.70%
发文量
0
审稿时长
>12 weeks
期刊介绍: Advances in Theoretical and Mathematical Physics is a bimonthly publication of the International Press, publishing papers on all areas in which theoretical physics and mathematics interact with each other.
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