Higgs bundles and SYZ geometry

2022/03/08 by Heller, Sebastian, Ouyang, Charles, Pedit, Franz
#Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric Topology (math.GT) #High Energy Physics - Theory (hep-th)

paper · doi:10.48550/arxiv.2203.04224

Abstract

Using non-Abelian Hodge theory for parabolic Higgs bundles, we construct infinitely many non-congruent hyperbolic affine spheres modeled on a thrice-punctured sphere with monodromy in SL₃(ℤ). These give rise to non-isometric semi-flat Calabi-Yau metrics on special Lagrangian torus bundles over an open ball in ℝ³ minus a Y-vertex, thereby answering a question raised by Loftin, Yau, and Zaslow in [LYZ], [LYZerr].

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