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62
Nonsupersymmetric Black Holes and Topological Strings
, 2007
"... We study nonsupersymmetric, extremal 4 dimensional black holes which arise upon compactification of type II superstrings on CalabiYau threefolds. We propose a generalization of the OSV conjecture for higher derivative corrections to the nonsupersymmetric black hole entropy, in terms of the one pa ..."
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We study nonsupersymmetric, extremal 4 dimensional black holes which arise upon compactification of type II superstrings on CalabiYau threefolds. We propose a generalization of the OSV conjecture for higher derivative corrections to the nonsupersymmetric black hole entropy, in terms of the one parameter refinement of topological string introduced by Nekrasov. We also study the attractor mechanism for nonsupersymmetric black holes and show how the inverse problem of fixing charges in terms of the attractor value of CY moduli can be explicitly solved.
Lectures on Spectrum Generating Symmetries and Uduality in Supergravity, Extremal Black Holes, Quantum Attractors and Harmonic Superspace
, 908
"... Abstract: We review the underlying algebraic structures of supergravity theories with symmetric scalar manifolds in five and four dimensions, orbits of their extremal black hole solutions and the spectrum generating extensions of their Uduality groups. For 5D, N = 2 MaxwellEinstein supergravity th ..."
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Cited by 13 (2 self)
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Abstract: We review the underlying algebraic structures of supergravity theories with symmetric scalar manifolds in five and four dimensions, orbits of their extremal black hole solutions and the spectrum generating extensions of their Uduality groups. For 5D, N = 2 MaxwellEinstein supergravity theories (MESGT) defined by Euclidean Jordan algebras,J, the spectrum generating symmetry groups are the conformal groups Conf(J) of J which are isomorphic to their Uduality groups in four dimensions. Similarly, the spectrum generating symmetry groups of 4D, N = 2 MESGTs are the quasiconformal groups QConf(J) associated with J that are isomorphic to their Uduality groups in three dimensions. We then review the work on spectrum generating symmetries of spherically symmetric stationary 4D BPS black holes, based on the equivalence of their attractor equations and the equations for geodesic motion of a fiducial particle on the target spaces of corresponding 3D supergravity theories obtained by timelike reduction. We also discuss the connection between harmonic superspace formulation of 4D, N = 2 sigma models coupled to supergravity and the minimal unitary representations of their isometry groups obtained by quantizing their quasiconformal realizations. We discuss the relevance of this connection to spectrum generating symmetries
Freudenthal triple classification of threequbit entanglement
, 2009
"... We show that the threequbit entanglement classes: (0) Null, (1) Separable ABC, (2a) Biseparable ABC, (2b) Biseparable BCA, (2c) Biseparable CAB, (3) W and (4) GHZ correspond respectively to ranks 0, 1, 2a, 2b, 2c, 3 and 4 of a Freudenthal triple system defined over the Jordan algebra C ⊕ C ⊕ C ..."
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Cited by 13 (3 self)
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We show that the threequbit entanglement classes: (0) Null, (1) Separable ABC, (2a) Biseparable ABC, (2b) Biseparable BCA, (2c) Biseparable CAB, (3) W and (4) GHZ correspond respectively to ranks 0, 1, 2a, 2b, 2c, 3 and 4 of a Freudenthal triple system defined over the Jordan algebra C ⊕ C ⊕ C. We also compute the corresponding SLOCC orbits.
Cargèse lectures on string theory with eight supercharges
 PROC. SUPPL. 171, 39 (2007)
, 2007
"... These lectures give an introduction to the interrelated topics of CalabiYau compactification of the type II string, black hole attractors, the allorders entropy formula, the dual (0,4) CFT, topological strings and the OSV conjecture. Based on notes by MG of lectures by AS at the 2006 Cargèse summe ..."
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Cited by 11 (0 self)
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These lectures give an introduction to the interrelated topics of CalabiYau compactification of the type II string, black hole attractors, the allorders entropy formula, the dual (0,4) CFT, topological strings and the OSV conjecture. Based on notes by MG of lectures by AS at the 2006 Cargèse summer school.
5d black holes and strings with higher derivatives
"... We find asymptotically flat black hole and string solutions to 5D supergravity in the presence of higher derivative terms. In some cases, including the fundamental heterotic string solution, the higher derivative terms smooth out naked singularities into regular geometries carrying zero entropy. We ..."
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Cited by 10 (2 self)
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We find asymptotically flat black hole and string solutions to 5D supergravity in the presence of higher derivative terms. In some cases, including the fundamental heterotic string solution, the higher derivative terms smooth out naked singularities into regular geometries carrying zero entropy. We also compute corrections to the entropy of 5D CalabiYau black holes, and discuss the relation to previous results.
String Theory Effects on FiveDimensional Black Hole Physics
, 2008
"... We review recent developments in understanding quantum/string corrections to BPS black holes and strings in fivedimensional supergravity. These objects are solutions to the effective action obtained from Mtheory compactified on a CalabiYau threefold, including the oneloop corrections determined ..."
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We review recent developments in understanding quantum/string corrections to BPS black holes and strings in fivedimensional supergravity. These objects are solutions to the effective action obtained from Mtheory compactified on a CalabiYau threefold, including the oneloop corrections determined by anomaly cancellation and supersymmetry. We introduce the offshell formulation of this theory obtained through the conformal supergravity method and review the methods for investigating supersymmetric solutions. This leads to quantum/string corrected attractor geometries, as well as asymptotically flat black strings and spinning black holes. With these solutions in hand, we compare our results with analogous studies in fourdimensional stringcorrected supergravity, emphasizing the distinctions between the four and five dimensional theories.
WIS/05/08FEBDPP 5D Black Holes and Nonlinear Sigma Models
, 802
"... Abstract: Stationary solutions of 5D supergravity with U(1) isometry can be efficiently studied by dimensional reduction to three dimensions, where they reduce to solutions to a locally supersymmetric nonlinear sigma model. We generalize this procedure to 5D gauged supergravity, and identify the co ..."
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Cited by 5 (1 self)
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Abstract: Stationary solutions of 5D supergravity with U(1) isometry can be efficiently studied by dimensional reduction to three dimensions, where they reduce to solutions to a locally supersymmetric nonlinear sigma model. We generalize this procedure to 5D gauged supergravity, and identify the corresponding gauging in 3D. We pay particular attention to the case where the Killing spinor is non constant along the fibration, which results, even for ungauged supergravity in 5D, in an additional gauging in 3D, without introducing any extra potential. We further study SU(2) × U(1) symmetric solutions, which correspond to geodesic motion on the sigma model (with potential in the gauged case). We identify and study the algebra of BPS constraints relevant for the BreckenridgeMyersPeetVafa black hole, the GutowskiReall black hole and several other BPS solutions, and obtain the corresponding radial wave functions in the semiclassical approximation. Unité mixte de recherche du CNRS UMR 7589 Unité mixte de recherche du CNRS UMR 8549Contents
Lectures on Mirror Symmetry and Topological String Theory
 Open Problems and Surveys of Contemporary Mathematics
"... These are notes of a series of lectures on mirror symmetry and topological string theory given at the Mathematical Sciences Center at Tsinghua University. The N = 2 superconformal algebra, its deformations and its chiral ring are reviewed. A topological field theory can be constructed whose observab ..."
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These are notes of a series of lectures on mirror symmetry and topological string theory given at the Mathematical Sciences Center at Tsinghua University. The N = 2 superconformal algebra, its deformations and its chiral ring are reviewed. A topological field theory can be constructed whose observables are only the elements of the chiral ring. When coupled to gravity, this leads to topological string theory. The identification of the topological string A and Bmodels by mirror symmetry leads to surprising connections in mathematics and provides tools for exact computations as well as new insights in physics. A recursive construction of the higher genus amplitudes of topological string theory expressed as polynomials is reviewed. 1 ar
Black holes admitting a Freudenthal dual
, 903
"... The quantised charges x of four dimensional stringy black holes may be assigned to elements of an integral Freudenthal triple system whose automorphism group is the corresponding Uduality and whose Uinvariant quartic norm ∆(x) determines the lowest order entropy. Here we introduce a Freudenthal du ..."
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The quantised charges x of four dimensional stringy black holes may be assigned to elements of an integral Freudenthal triple system whose automorphism group is the corresponding Uduality and whose Uinvariant quartic norm ∆(x) determines the lowest order entropy. Here we introduce a Freudenthal duality x → ˜x, for which ˜x = −x. Although distinct from Uduality it nevertheless leaves ∆(x) invariant. However, the requirement that ˜x be integer restricts us to the subset of black holes for which ∆(x) is necessarily a perfect square. The issue of higherorder corrections remains open as some, but not all, of the discrete Uduality invariants are Freudenthal invariant. Similarly, the quantised charges A of five dimensional black holes and strings may be assigned to elements of an integral Jordan algebra, whose cubic norm N(A) determines the lowest order entropy. We introduce an analogous Jordan dual A ⋆ , with N(A) necessarily a perfect cube, for which A ⋆ ⋆ = A and which leaves N(A) invariant. The two dualities