Ricci-flat metrics on vector bundles over flag manifolds

Dmitri Bykov; Ismail Achmed-Zade

Ricci-flat metrics on vector bundles over flag manifolds

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arxiv 1905.00412 v1 pith:LFZ52ZFG submitted 2019-05-01 hep-th math.DG

Ismail Achmed-Zade , Dmitri Bykov This is my paper · ORCID

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keywords metricsbundlesflagmanifoldscanonicalmathbbricci-flatvector

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abstract

We construct explicit complete Ricci-flat metrics on the total spaces of certain vector bundles over flag manifolds of the group $SU(n)$, for all K\"ahler classes. These metrics are natural generalizations of the metrics of Candelas-de la Ossa on the conifold, Pando Zayas-Tseytlin on the canonical bundle over $\mathbb{CP}^1\times \mathbb{CP}^1$, as well as the metrics on canonical bundles over flag manifolds, recently constructed by van Coevering.

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Ricci-flat metrics from gauged linear $\sigma$-models without RG flow
hep-th 2026-08 conditional novelty 7.0 of 10

Explicit Ricci-flat Kähler metrics on cones over products of projective spaces are built from gauged linear sigma models whose 'shadow' fields carry negative-signature kinetic terms.

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