Hermitian-Einstein metrics from noncommutative \(U\left(1 \right)\) instantons

We show that Hermitian-Einstein metrics can be locally constructed by a map from (anti-)self-dual two-forms on Euclidean \({\mathbb R}^4\) to symmetric two-tensors introduced in "Gravitational instantons from gauge theory," H. S. Yang and M. Salizzoni, Phys. Rev. Lett. (2006) 201602, [hep-...

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Bibliographic Details
Published inarXiv.org
Main Authors Hara, Kentaro, Sako, Akifumi, Yang, Hyun Seok
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 07.09.2018
Subjects
Gauge theory
Gravitation theory
Instantons
Tensors
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Summary:We show that Hermitian-Einstein metrics can be locally constructed by a map from (anti-)self-dual two-forms on Euclidean \({\mathbb R}^4\) to symmetric two-tensors introduced in "Gravitational instantons from gauge theory," H. S. Yang and M. Salizzoni, Phys. Rev. Lett. (2006) 201602, [hep-th/0512215]. This correspondence is valid not only for a commutative space but also for a noncommutative space. We choose \(U(1)\) instantons on a noncommutative \({\mathbb C}^2\) as the self-dual two-form, from which we derive a family of Hermitian-Einstein metrics. We also discuss the condition when the metric becomes K\"ahler.
ISSN:2331-8422
DOI:10.48550/arxiv.1809.02328