Examples of deformed Spin(7)-instantons/Donaldson-Thomas connections

Udhav Fowdar

Examples of deformed Spin(7)-instantons/Donaldson-Thomas connections

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arxiv 2311.11794 v2 pith:BOW75PA3 submitted 2023-11-20 math.DG

Udhav Fowdar This is my paper · ORCID

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abstract

We construct examples of deformed Hermitian Yang-Mills connections and deformed Spin(7)-instantons (also called Spin(7) deformed Donaldson-Thomas connections) on the cotangent bundle of $\mathbb{C}\mathbb{P}^2$ endowed with the Calabi hyperK\"ahler structure. Deformed Spin(7)-instantons on cones over 3-Sasakian 7-manifolds are also constructed. We show that these can be used to distinguish between isometric structures and also between Sp(2) and Spin(7) holonomy cones. To the best of our knowledge, these are the first non-trivial examples of deformed Spin(7)-instantons.

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Deformed Hermitian-Yang-Mills equation on the manifold of full flags
math.DG 2026-07 accept novelty 7.0 of 10

First irreducible rank-2 dHYM connections are constructed on the full flag manifold F₂, and rank-1 solutions outside the supercritical regime disprove conjectured stability conditions.

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