D-instantons and twistors

Abstract

Finding the exact, quantum corrected metric on the hypermultiplet moduli space in Type II string compactifications on Calabi-Yau threefolds is an outstanding open problem. We address this issue by relating the quaternionic-Kahler metric on the hypermultiplet moduli space to the complex contact geometry on its twistor space. In this framework, Euclidean D-brane instantons are captured by contact transformations between different patches. We derive those by recasting the previously known A-type D2-instanton corrections in the language of contact geometry, covariantizing the result under electro-magnetic duality, and using mirror symmetry. As a result, we are able to express the effects of all D-instantons in Type II compactifications concisely as a sum of dilogarithm functions. We conclude with some comments on the relation to microscopic degeneracies of four-dimensional BPS black holes and to the wall-crossing formula of Kontsevich and Soibelman, and on the form of the yet unknown NS5-brane instanton contributions.

47 pages, 1 figure, uses JHEP3.cls

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• Instantons and infinite distances
• $R^4$ couplings and automorphic unipotent representations
• Instanton Corrections and Emergent Strings
• Twistor Approach to String Compactifications: a Review
• The Higgs mass from a String-Theoretic Perspective
• D3-instantons, Mock Theta Series and Twistors
• Fivebrane instantons, topological wave functions and hypermultiplet moduli spaces
• Linear perturbations of quaternionic metrics
• Multiple D3-instantons and mock modular forms I
• Infinite Distances and the Axion Weak Gravity Conjecture
• Wall-crossing, Rogers dilogarithm, and the QK/HK correspondence
• Completeness in supergravity constructions
• Four ways across the wall
• D-instantons in Type IIA string theory on Calabi-Yau threefolds
• Quantum mirror symmetry and twistors
• Type II/F-theory Superpotentials with Several Deformations and N=1 Mirror Symmetry
• Self-dual Einstein Spaces, Heavenly Metrics and Twistors
• Euclidean D-branes in Type IIB string theory on Calabi-Yau threefolds
• The Hesse potential, the c-map and black hole solutions
• Exponential BPS graphs and D brane counting on toric Calabi-Yau threefolds: Part I
• Exploring 5d BPS Spectra with Exponential Networks
• Five-dimensional gauge theory and compactification on a torus
• Mathematical structures of non-perturbative topological string theory: from GW to DT invariants
• Large D-instanton effects in string theory
• D-instanton Induced Superpotential
• $R^3$ index for four-dimensional $N=2$ field theories
• S-duality in Twistor Space
• S-duality and refined BPS indices
• Multiple D3-instantons and mock modular forms II
• Dualities and fivebrane instantons
• On the topology of the hypermultiplet moduli space in type II/CY string vacua
• Hypermultiplet metric and D-instantons
• Non-perturbative effects and wall-crossing from topological strings
• Fivebrane instantons in Calabi-Yau compactifications
• Wall-crossing made smooth
• Rigid limit for hypermultiplets and five-dimensional gauge theories
• TBA for non-perturbative moduli spaces
• Black holes and higher depth mock modular forms
• A 5d/2d/4d correspondence
• Automorphic Instanton Partition Functions on Calabi-Yau Threefolds
• Conformal TBA for resolved conifolds
• Heavenly metrics, BPS indices and twistors
• Borcherds Algebras and N=4 Topological Amplitudes
• Gauge Threshold Corrections for N = 2 Heterotic Local Models with Flux, and Mock Modular Forms
• Scaling Black Holes and Modularity
• Quaternionic Kähler metrics associated to special Kähler manifolds with mutually local variations of BPS structures
• Modularity, Quaternion-Kahler spaces and Mirror Symmetry
• BPS Spectrum, Indices and Wall Crossing in N=4 Supersymmetric Yang-Mills Theories
• Heterotic-Type II duality in the hypermultiplet sector
• Heterotic-type II duality in twistor space
• Instantons and Wormholes in N=2 supergravity
• Developments in special geometry
• Hypermultiplet metric and NS5-instantons
• c-map as c=1 string
• Darboux Coordinates and Instanton Corrections in Projective Superspace
• Refinement and modularity of immortal dyons
• Mock modularity at work, or black holes in a forest
• Non-perturbative scalar potential inspired by type IIA strings on rigid CY
• Resurgence of Refined Topological Strings and Dual Partition Functions
• S-duality and the universal isometries of instanton corrected q-map spaces
• S-duality and the universal isometries of q-map spaces
• Quantum TBA for refined BPS indices
• Symmetries of non-maximal supergravities with higher-derivative corrections