Local B-model and Mixed Hodge Structure
Yukiko Konishi, Satoshi Minabe
TL;DR
This paper explores the mixed Hodge structures in the local B-model of mirror symmetry, defining a Yukawa coupling analogue and analyzing a local holomorphic anomaly equation.
Contribution
It introduces a new mixed Hodge theoretic framework for the local B-model and formulates a local holomorphic anomaly equation.
Findings
Defined an analogue of the Yukawa coupling using mixed Hodge structures
Described a local version of the holomorphic anomaly equation
Provided insights into the Hodge theoretic aspects of local mirror symmetry
Abstract
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.
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Taxonomy
TopicsBlack Holes and Theoretical Physics · Nonlinear Waves and Solitons · Algebraic Geometry and Number Theory