2025/01/07 by Baldwin, Daniel Andrew, Acharya, Bobby Samir
#Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th)
paper · doi:10.48550/arxiv.2501.03692
HyperKähler 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 hyperKähler 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 hyperKähler 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.