物理学中的混合Hodge结构与重正化

Local B-model and Mixed Hodge Structure

We study the mixed Hodge theoretic aspects of the B-model side of local mirror symmetry. Our main objectives are to define an analogue of the Yukawa coupling in terms of the variations of the mixed Hodge structures and to study its properties. We also describe a local version of Bershadsky-Cecotti-Ooguri-Vafa's holomorphic anomaly equation.

锥点退化中的Hodge原子：F-丛、极限混合Hodge模与刚柔分解

Hodge Atoms at Conifold Degenerations: F-Bundles, Limiting Mixed Hodge Modules, and the Rigid-Flexible Decomposition

研究锥点退化中Calabi-Yau三fold的Hodge原子分解，通过刚柔分解构造修正的混合Hodge模，并利用Stokes-扩展识别确定非分裂结构。

Mixed Hodge structure and $\mathcal{N}=2$ Coulomb branch solution

The Coulomb branch of four dimensional $\mathcal{N}=2$ theories can be solved by finding a Seiberg-Witten (SW) geometry and a SW differential. While lots of SW geometries are found, the extraction of low energy theory out of it is limited due to following reasons: (a) the difficulty of distinguishing electric-magnetic and flavor charges; (b) the difficulty of determining the low energy theory at singular point; (c) the lack of SW differential. We show that the mixed Hodge structure (MHS) can be used to fully solve the low energy physics of Coulomb branch at every vacuum. The MHS can be used to…

几何跃迁与混合Hodge结构

Geometric Transitions and Mixed Hodge Structures

利用Hodge结构的退化，给出并证明了紧致Calabi-Yau空间之间一般锥型跃迁的B-模型圆盘级大N对偶结果.

The physics and the mixed Hodge structure of Feynman integrals

This expository text is an invitation to the relation between quantum field theory Feynman integrals and periods. We first describe the relation between the Feynman parametrization of loop amplitudes and world-line methods, by explaining that the first Symanzik polynomial is the determinant of the period matrix of the graph, and the second Symanzik polynomial is expressed in terms of world-line Green's functions. We then review the relation between Feynman graphs and variations of mixed Hodge structures. Finally, we provide an algorithm for generating the Picard-Fuchs equation satisfied by the…

正几何与典范形式：混合Hodge理论视角

Positive geometries and canonical forms via mixed Hodge theory

本文用混合Hodge理论重新表述正几何及其典范形式，提出亏格零对作为统一框架，证明相关基本性质，并详析超平面排列与凸多胞形案例。