立方椭圆球面的属二 G 函数与模块性

IF 1.3 3区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Letters in Mathematical Physics Pub Date : 2024-05-27 DOI:10.1007/s11005-024-01818-8

Xin Wang

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引用次数: 0

摘要

本文研究了 Dubrovin、Liu 和 Zhang 针对立方椭圆轨道提出的属二 G 函数。作为结果，我们首先证明了所有属中某类后裔相关函数的准模块性。然后，我们证明了一定类型的属二 G 函数的任何导数都是镜像变换后的准模态形式。特别是，我们计算了其特定一阶导数的显式封闭公式。我们的证明主要依靠两种技术：半简单弗罗贝尼斯流形的 Givental 量化形式主义和稳定曲线模空间的同调关系。

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The genus two G-function for cubic elliptic orbifold and modularity

In this paper, we study the genus two G-function which was introduced by Dubrovin, Liu and Zhang for the cubic elliptic orbifold. As results, we first prove the quasi-modularity for the descendant correlation functions of certain type in all genus. Then we prove any derivatives of the genus two G-function of certain type are quasi-modular forms after a mirror transformation. In particular, we compute the explicit closed formula for its certain first derivative. Our proof mainly relies on two techniques: Givental quantization formalism for semisimple Frobenius manifold and the tautological relations on the moduli space of stable curves.

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来源期刊

Letters in Mathematical Physics 物理-物理：数学物理

CiteScore

2.40

自引率

8.30%

发文量

111

审稿时长

3 months

期刊介绍： The aim of Letters in Mathematical Physics is to attract the community''s attention on important and original developments in the area of mathematical physics and contemporary theoretical physics. The journal publishes letters and longer research articles, occasionally also articles containing topical reviews. We are committed to both fast publication and careful refereeing. In addition, the journal offers important contributions to modern mathematics in fields which have a potential physical application, and important developments in theoretical physics which have potential mathematical impact.