Quaternionic Kähler metrics associated to special Kähler manifolds with mutually local variations of BPS structures

Abstract

We construct a quaternionic-Kähler manifold from a conical special Kähler manifold with a certain type of mutually-local variation of BPS structures. We give global and local explicit formulas for the quaternionic-Kähler metric, and specify under which conditions it is positive-definite. Locally, the metric is a deformation of the 1-loop corrected Ferrara-Sabharval metric obtained via the supergravity c-map. The type of quaternionic-Kähler metrics we obtain are related to work in the physics literature by S. Alexandrov and S. Banerjee, where they discuss the hypermultiplet moduli space metric of type IIA string theory, with mutually local D-instanton corrections.

31 pages. Typos fixed and improved presentation based on the suggestions by the referees. Final version to appear in Annales Henri Poincaré

References in corpus (8)

• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• String loop corrected hypermultiplet moduli spaces
• D-instantons and twistors
• HyperKahler and quaternionic Kahler manifolds with S^1-symmetries
• Special Geometry of Euclidean Supersymmetry III: the local r-map, instantons and black holes
• $R^3$ index for four-dimensional $N=2$ field theories
• Hypermultiplet metric and D-instantons
• Complete quaternionic Kähler manifolds with finite volume ends

Cited by in corpus (7)

• D-instantons in Type IIA string theory on Calabi-Yau threefolds
• Mathematical structures of non-perturbative topological string theory: from GW to DT invariants
• Hypermultiplet metric and NS5-instantons
• A Hyperkähler geometry associated to the BPS structure of the resolved conifold
• S-duality and the universal isometries of instanton corrected q-map spaces
• S-duality and the universal isometries of q-map spaces
• Special Joyce structures and hyperkähler metrics