XXXVIII Workshop on Geometric Methods in Physics 30.06-6.07.2019 VIII School on Geometry and Physics 24-28.06.2019
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# Kentaro Hara

## Hermitian–Einstein metrics from noncommutative $U(1)$ solutions

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 C2 as the self–dual two–form, from which we derive a family of Hermitian–Einstein metrics. We also discuss the condition when the two–forms are not instantons but they are solutions to the Yang–Mills equations.

 Event sponsored by: University of Bialystok

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