Twistors and Black Holes
arXiv:hep-th/0701214 · doi:10.1088/1126-6708/2007/04/038
Abstract
Motivated by black hole physics in N=2, D=4 supergravity, we study the geometry of quaternionic-Kahler manifolds M obtained by the c-map construction from projective special Kahler manifolds M_s. Improving on earlier treatments, we compute the Kahler potentials on the twistor space Z and Swann space S in the complex coordinates adapted to the Heisenberg symmetries. The results bear a simple relation to the Hesse potential Σof the special Kahler manifold M_s, and hence to the Bekenstein-Hawking entropy for BPS black holes. We explicitly construct the ``covariant c-map'' and the ``twistor map'', which relate real coordinates on M x CP^1 (resp. M x R^4/Z_2) to complex coordinates on Z (resp. S). As applications, we solve for the general BPS geodesic motion on M, and provide explicit integral formulae for the quaternionic Penrose transform relating elements of H^1(Z,O(-k)) to massless fields on M annihilated by first or second order differential operators. Finally, we compute the exact radial wave function (in the supergravity approximation) for BPS black holes with fixed electric and magnetic charges.
47 pages, v2: typos corrected, reference added, v3: minor changes
References in corpus (28)
- Black Hole Entropy in M-Theory
- Black Hole Attractors and the Topological String
- Black Holes and Critical Points in Moduli Space
- Supergravity flows and D-brane stability
- Exact solutions for supersymmetric stationary black hole composites
- Hartle-Hawking Wave-Function for Flux Compactifications
- String loop corrected hypermultiplet moduli spaces
- Superconformal Hypermultiplets
- Conformal and Quasiconformal Realizations of Exceptional Lie Groups
- Superconformal N=2, D=5 matter with and without actions
- Black hole partition functions and duality
- Lectures on on Black Holes, Topological Strings and Quantum Attractors (2.0)
- Hypermultiplets, Hyperkahler Cones and Quaternion-Kahler Geometry
- BPS black holes, quantum attractor flows and automorphic forms
- Hypermultiplets and Topological Strings
- General Static N=2 Black Holes
- Quantum Attractor Flows
- Special geometry of Euclidean supersymmetry II: hypermultiplets and the c-map
- Black holes in N=2 supergravity theories and harmonic functions
- Off-shell N=2 tensor supermultiplets
- Supergravity Instantons for N=2 Hypermultiplets
- From Type IIA Black Holes to T-dual Type IIB D-Instantons in N=2, D=4 Supergravity
- The map between conformal hypercomplex/hyper-Kaehler and quaternionic(-Kaehler) geometry
- Supergravity description of spacetime instantons
- Conformal Compensators and Manifest Type IIB S-Duality
- Quaternion-Kahler spaces, hyperkahler cones, and the c-map
- Observations on the Darboux coordinates for rigid special geometry
- The identification of conformal hypercomplex and quaternionic manifolds
Cited by in corpus (52)
- Four-dimensional wall-crossing via three-dimensional field theory
- Non-Supersymmetric Attractor Flow in Symmetric Spaces
- Nonperturbative corrections to 4D string theory effective actions from SL(2,Z) duality and supersymmetry
- Generating Geodesic Flows and Supergravity Solutions
- Instantons and infinite distances
- D-instantons and twistors
- Small Cosmological Constants in String Theory
- Extremal black holes, nilpotent orbits and the true fake superpotential
- Quantum Attractor Flows
- Different representations for the action principle in 4D N = 2 supergravity
- Twistor Approach to String Compactifications: a Review
- D-instantons and twistors: some exact results
- E7(7) formulation of N=2 backgrounds
- D3-instantons, Mock Theta Series and Twistors
- Fivebrane instantons, topological wave functions and hypermultiplet moduli spaces
- Linear perturbations of quaternionic metrics
- Wall-crossing, Rogers dilogarithm, and the QK/HK correspondence
- Quantum mirror symmetry and twistors
- Self-dual Einstein Spaces, Heavenly Metrics and Twistors
- The Hesse potential, the c-map and black hole solutions
- The N=1 Low-Energy Effective Action of Spontaneously Broken N=2 Supergravities
- Quasi-conformal actions, quaternionic discrete series and twistors: SU(2,1) and G_2(2)
- Quantum covariant c-map
- Large D-instanton effects in string theory
- S-duality in Twistor Space
- Spectrum Generating Conformal and Quasiconformal U-Duality Groups, Supergravity and Spherical Vectors
- 5D Black Holes and Non-linear Sigma Models
- Instantons, Hypermultiplets and the Heterotic String
- Conifold singularities, resumming instantons and non-perturbative mirror symmetry
- Twistor actions for gauge theory and gravity
- Lectures on Spectrum Generating Symmetries and U-duality in Supergravity, Extremal Black Holes, Quantum Attractors and Harmonic Superspace
- Automorphic Instanton Partition Functions on Calabi-Yau Threefolds
- New extended superconformal sigma models and Quaternion Kahler manifolds
- N=4 BPS black holes and octonionic twistors
- Finite and infinite-dimensional symmetries of pure N=2 supergravity in D=4
- Quaternion-Kaehler four-manifolds and Przanowski's function
- Modularity, Quaternion-Kahler spaces and Mirror Symmetry
- Heterotic-type II duality in twistor space
- Recent results in four-dimensional non-perturbative string theory
- Hypermultiplet metric and NS5-instantons
- c-map as c=1 string
- Quaternionic Kaehler Detour Complexes & N=2 Supersymmetric Black Holes
- A note on conformal symmetry in projective superspace
- Higher Derivative Corrections, Dimensional Reduction and Ehlers Duality
- The moduli space of hyper-K{ä}hler four-fold compactifications
- S-duality and the universal isometries of instanton corrected q-map spaces
- On quaternionic complexes over unimodular quaternionic manifolds
- Calabi-Yau compactification of type II string theories
- Quaternionic Kahler spaces with large toric symmetry
- An analogue of the Gibbons-Hawking Ansatz for quaternionic Kähler spaces
- S-duality and the universal isometries of q-map spaces
- Towards the Core of the Quantum Monopole