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45
Extremal Black Hole and Flux Vacua Attractors
, 2007
"... These lectures provide a pedagogical, introductory review of the socalled Attractor Mechanism (AM) at work in two different 4dimensional frameworks: extremal black holes in N = 2 supergravity and N = 1 flux compactifications. In the first case, AM determines the stabilization of scalars at the bla ..."
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Cited by 23 (15 self)
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These lectures provide a pedagogical, introductory review of the socalled Attractor Mechanism (AM) at work in two different 4dimensional frameworks: extremal black holes in N = 2 supergravity and N = 1 flux compactifications. In the first case, AM determines the stabilization of scalars at the black hole event horizon purely in terms of the electric and magnetic charges, whereas in the second context the AM is responsible for the stabilization of the universal axiondilaton and of the (complex structure) moduli purely in terms of the RR and NSNS fluxes. Two equivalent approaches to AM, namely the socalled “criticality conditions ” and “New Attractor ” ones, are analyzed in detail in both frameworks, whose analogies and differences are discussed. Also a stringy analysis of both frameworks (relying on Hodgedecomposition techniques) is performed, respectively considering 2 CY3×T Type IIB compactified on CY3 and its orientifolded version, associated with. Finally, recent Z2 results on the Uduality orbits and moduli spaces of nonBPS extremal black hole attractors in
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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Cited by 18 (1 self)
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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.
The M5brane elliptic genus: Modularity and BPS states,” arXiv:hepth/0607010
"... The modified elliptic genus for an M5brane wrapped on a fourcycle of a CalabiYau threefold encodes the degeneracies of an infinite set of BPS states in four dimensions. By holomorphy and modular invariance, it can be determined completely from the knowledge of a finite set of such BPS states. We ..."
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Cited by 18 (2 self)
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The modified elliptic genus for an M5brane wrapped on a fourcycle of a CalabiYau threefold encodes the degeneracies of an infinite set of BPS states in four dimensions. By holomorphy and modular invariance, it can be determined completely from the knowledge of a finite set of such BPS states. We show the feasibility of such a computation and determine the exact modified elliptic genus for an M5brane wrapping a hyperplane section of the quintic threefold.
Extended Holomorphic Anomaly and Loop Amplitudes in Open Topological String
 JEFFERSON PHYSICAL LABORATORY, HARVARD UNIVERSITY, 17 OXFORD ST
, 2007
"... Open topological string amplitudes on compact CalabiYau threefolds are shown to satisfy an extension of the holomorphic anomaly equation of Bershadsky, Cecotti, Ooguri and Vafa. The total topological charge of the Dbrane configuration must vanish in order to satisfy tadpole cancellation. The bound ..."
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Cited by 16 (1 self)
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Open topological string amplitudes on compact CalabiYau threefolds are shown to satisfy an extension of the holomorphic anomaly equation of Bershadsky, Cecotti, Ooguri and Vafa. The total topological charge of the Dbrane configuration must vanish in order to satisfy tadpole cancellation. The boundary state of such Dbranes is holomorphically captured by a Hodge theoretic normal function. Its Griffiths’ infinitesimal invariant is the analogue of the closed string Yukawa coupling and plays the role of the terminator in a Feynman diagram expansion for the topological string with Dbranes. The holomorphic anomaly equation is solved and the holomorphic ambiguity is fixed for some representative worldsheets of low genus and with few boundaries on
The Wave Function Behavior of the Open Topological String Partition Function On The Conifold
, 2007
"... We calculate the topological string partition function to all genus on the conifold, in the presence of branes. We demonstrate that the partition functions for different brane backgrounds (smoothly connected along a quantum corrected moduli space) can be interpreted as the same wave function in diff ..."
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Cited by 16 (1 self)
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We calculate the topological string partition function to all genus on the conifold, in the presence of branes. We demonstrate that the partition functions for different brane backgrounds (smoothly connected along a quantum corrected moduli space) can be interpreted as the same wave function in different polarizations. This behavior has a natural interpretation in the ChernSimons target space description of the topological theory. Our detailed analysis however indicates that nonperturbatively, a modification of real ChernSimons theory is required to capture the correct target space theory of the topological string. We perform our calculations in the framework of a free fermion representation of the open topological string, demonstrating that this framework extends beyond the simple C³ geometry. The notion of a fermionic brane creation operator arises in this setting, and we study to what extent the wave function properties of the
Background Independence and the Open Topological String Wavefunction
, 2007
"... The open topological string partition function in the background of a Dbrane on a CalabiYau threefold specifies a state in the Hilbert space associated with the quantization of the underlying special geometry. This statement is a consequence of the extended holomorphic anomaly equation after an ap ..."
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Cited by 12 (2 self)
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The open topological string partition function in the background of a Dbrane on a CalabiYau threefold specifies a state in the Hilbert space associated with the quantization of the underlying special geometry. This statement is a consequence of the extended holomorphic anomaly equation after an appropriate shift of the closed string variables, and can be viewed as the expression of background independence for the openclosed topological string. We also clarify various other aspects of the structure of the extended holomorphic anomaly equation. We conjecture that the collection of all Dbranes furnishes a basis of the Hilbert space, and revisit the BPS interpretation of the open topological string wavefunction in this light.
Evidence for Tadpole Cancellation in the Topological String
, 2009
"... We study the topological string on compact CalabiYau threefolds in the presence of orientifolds and Dbranes. In examples, we find that the total topological string amplitude admits a BPS expansion only if the topological charge of the Dbrane configuration is equal to that of the orientifold plane ..."
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Cited by 12 (3 self)
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We study the topological string on compact CalabiYau threefolds in the presence of orientifolds and Dbranes. In examples, we find that the total topological string amplitude admits a BPS expansion only if the topological charge of the Dbrane configuration is equal to that of the orientifold plane. We interpret this as a manifestation of a general tadpole cancellation condition in the topological string that is necessary for decoupling of A and Bmodel in loop amplitudes. Our calculations in the Amodel involve an adapted version of existing localization techniques, and give predictions for the real enumerative geometry of higher genus curves in CalabiYau manifolds. In the Bmodel, we introduce an extension of the holomorphic anomaly equation to unoriented
String theory and the Kauffman polynomial
, 2009
"... We give a new, precise integrality conjecture for the colored Kauffman polynomial of knots and links inspired by large N dualities and the structure of topological string theory on orientifolds. According to this conjecture, the natural knot invariant to consider in an unoriented theory involves bot ..."
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Cited by 8 (0 self)
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We give a new, precise integrality conjecture for the colored Kauffman polynomial of knots and links inspired by large N dualities and the structure of topological string theory on orientifolds. According to this conjecture, the natural knot invariant to consider in an unoriented theory involves both the colored Kauffman polynomial and the colored HOMFLY polynomial for composite representations, i.e. it involves the full HOMFLY skein of the annulus. The conjecture sheds new light on the relationship between the Kauffman and the HOMFLY polynomials, and it implies for example Rudolph’s theorem. We provide various nontrivial tests of the conjecture and we sketch the string theory
A comment on quantum distribution functions
 and the OSV conjecture,” JHEP 0612 (2006) 069 [arXiv:hepth/0608162
"... Abstract: Using the attractor mechanism and the relation between the quantization of H 3 (M) and topological strings on a Calabi Yau threefold M we define a map from BPS black holes into coherent states. This map allows us to represent the BekensteinHawkingWald entropy as a quantum distribution fu ..."
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Cited by 4 (1 self)
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Abstract: Using the attractor mechanism and the relation between the quantization of H 3 (M) and topological strings on a Calabi Yau threefold M we define a map from BPS black holes into coherent states. This map allows us to represent the BekensteinHawkingWald entropy as a quantum distribution function on the phase space H 3 (M). This distribution function is a mixed Husimi/antiHusimi distribution corresponding to the different normal ordering prescriptions for the string coupling and deviations of the complex structure moduli. From the integral representation of this distribution function in terms of the Wigner distribution we recover the OoguriStromingerVafa (OSV) conjecture in the region “at infinity ” of the complex structure moduli space. The physical meaning of the OSV corrections are briefly