Modularity, Quaternion-Kahler spaces and Mirror Symmetry

Abstract

We provide an explicit twistorial construction of quaternion-Kahler manifolds obtained by deformation of c-map spaces and carrying an isometric action of the modular group SL(2,Z). The deformation is not assumed to preserve any continuous isometry and therefore this construction presents a general framework for describing NS5-brane instanton effects in string compactifications with N=2 supersymmetry. In this context the modular invariant parametrization of twistor lines found in this work yields the complete non-perturbative mirror map between type IIA and type IIB physical fields.

28 pages; added some clarifications; corrected misprint in the S-duality constraint (4.8)

References in corpus (10)

• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• String loop corrected hypermultiplet moduli spaces
• Nonperturbative corrections to 4D string theory effective actions from SL(2,Z) duality and supersymmetry
• D-instantons and twistors
• D3-instantons, Mock Theta Series and Twistors
• Quantum mirror symmetry and twistors
• Linear perturbations of Hyperkahler metrics
• S-duality in Twistor Space
• Quantum hypermultiplet moduli spaces in N=2 string vacua: a review
• Quaternion-Kahler spaces, hyperkahler cones, and the c-map

Cited by in corpus (8)

• Multiple D3-instantons and mock modular forms I
• Membrane Limits in Quantum Gravity
• Dualities and fivebrane instantons
• Hypermultiplet metric and D-instantons
• Fivebrane instantons in Calabi-Yau compactifications
• Black holes and higher depth mock modular forms
• Hypermultiplet metric and NS5-instantons
• Quantum Curve for strip geometries, Topological Recursion and open GW/DT invariants