Papers › On Classifying HyperKähler Kummer 8-Orbifolds
On Classifying HyperKähler Kummer 8-Orbifolds
Daniel Andrew Baldwin, Bobby Samir Acharya
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HyperK\"ahler spaces, including manifolds, orbifolds and conical singularities play an important role in superstring/M-theory and gauge theories as well as in differential and algebraic geometry. In this paper we provide hundreds of new examples of compact hyperK\"ahler orbifolds of Kummer type T⁸/G, where T⁸ is the maximal torus of the compact Lie group E₈ and G a finite group of isometries whose holonomies form a subgroup of the Weyl group of E₈. We show that, out of all of these examples, the only orbifolds whose singularities have a known holomorphic symplectic resolution lead to manifolds diffeomorphic to the two currently known examples of compact hyperK\"ahler 8-manifolds. We also demonstrate that these methods can, when combined with theorems of Joyce, be extended to construct potentially new manifolds of SU(4)- and Spin(7)- holonomy. All of these examples give rise to new vacua of string/M-theory in two/three dimensions.
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