TL;DR
This paper introduces a novel construction of bundles on K3 surfaces, exploring their relation to Hitchin's equations, mirror symmetry, and potential dualities between bundles on mirror K3s.
Contribution
It presents a new method for constructing bundles on Calabi-Yau manifolds, specifically K3 surfaces, and investigates their connections to mirror symmetry and dualities.
Findings
Provides plausibility arguments linking Hitchin's solutions to bundle moduli spaces on K3s
Shows that Vafa's mirror data can specify bundles on mirror K3s
Suggests a potential duality between bundles on mirror K3 surfaces
Abstract
In this technical note we describe a new (to the physics literature) construction of bundles on Calabi-Yaus. We primarily study this construction in the special case of K3 surfaces, for which interesting results can be obtained. For example, we use this construction to give plausibility arguments for a relationship between spaces of solutions of Hitchin's equations and moduli spaces of bundles on K3s. Also, in a recent paper it was proposed by C. Vafa that the mirror to a bundle on a Calabi-Yau n-fold is, in a particular sense, a supersymmetric n-cycle on the mirror Calabi-Yau. We use this new construction to observe that for the special case of K3s, Vafa's mirror data also specifies a bundle directly on the mirror K3, and so we potentially have a duality between bundles on any one K3 and other bundles on the mirror K3.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometry and complex manifolds · Advanced Algebra and Geometry