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225
Split States, Entropy Enigmas, Holes and Halos
, 2007
"... We investigate degeneracies of BPS states of Dbranes on compact CalabiYau manifolds. We develop a factorization formula for BPS indices using attractor flow trees associated to multicentered black hole bound states. This enables us to study background dependence of the BPS spectrum, to compute e ..."
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Cited by 235 (22 self)
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We investigate degeneracies of BPS states of Dbranes on compact CalabiYau manifolds. We develop a factorization formula for BPS indices using attractor flow trees associated to multicentered black hole bound states. This enables us to study background dependence of the BPS spectrum, to compute explicitly exact indices of various nontrivial Dbrane systems, and to clarify the subtle relation of DonaldsonThomas invariants to BPS indices of stable D6D2D0 states, realized in supergravity as “hole halos. ” We introduce a convergent generating function for D4 indices in the large CY volume limit, and prove it can be written as a modular average of its polar part, generalizing the fareytail expansion of the elliptic genus. We show polar states are “split ” D6antiD6 bound states, and that the partition function factorizes accordingly, leading to a refined version of the OSV conjecture. This differs from the original conjecture in several aspects. In particular we obtain a nontrivial measure factor g −2 top e−K and find factorization requires a cutoff. We show that the main factor determining the cutoff and therefore the error is the existence of “swing states ” — D6 states which exist at large radius but do not form stable D6antiD6 bound states. We point out a likely breakdown of the OSV conjecture at small gtop (in the large background CY volume limit), due to the surprising phenomenon that for sufficiently large background Kähler moduli, a charge ΛΓ supporting single centered black holes of entropy ∼ Λ2S(Γ) also admits twocentered BPS black hole realizations whose entropy grows like Λ3 when Λ → ∞.
DBranes on CalabiYau Spaces and Their Mirrors
, 1996
"... We study the boundary states of Dbranes wrapped around supersymmetric cycles in a general CalabiYau manifold. In particular, we show how the geometric data on the cycles are encoded in the boundary states. As an application, we analyze how the mirror symmetry transforms Dbranes, and we verify tha ..."
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Cited by 185 (11 self)
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We study the boundary states of Dbranes wrapped around supersymmetric cycles in a general CalabiYau manifold. In particular, we show how the geometric data on the cycles are encoded in the boundary states. As an application, we analyze how the mirror symmetry transforms Dbranes, and we verify that it is consistent with the conjectured periodicity and the monodromy of the RamondRamond field configuration on a CalabiYau manifold. This also enables us to study open string worldsheet instanton corrections and relate them to closed string instanton counting. The cases when the mirror symmetry is realized as Tduality are also discussed. Permanent address: Department of Particle Physics, Weizmann Institute of Science, 76100 Rehovot Israel. 1 Introduction Dbranes in type II string theories have been identified as RamondRamond charged BPS states [1]. In the presence of a Dbrane, the boundary conditions for open strings are modified in such a way that Dirichlet boundary conditions ...
The topological vertex
, 2003
"... We construct a cubic field theory which provides all genus amplitudes of the topological Amodel for all noncompact toric CalabiYau threefolds. The topology of a given Feynman diagram encodes the topology of a fixed CalabiYau, with Schwinger parameters playing the role of Kähler classes of the th ..."
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Cited by 167 (25 self)
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We construct a cubic field theory which provides all genus amplitudes of the topological Amodel for all noncompact toric CalabiYau threefolds. The topology of a given Feynman diagram encodes the topology of a fixed CalabiYau, with Schwinger parameters playing the role of Kähler classes of the threefold. We interpret this result as an operatorial computation of the amplitudes in the Bmodel mirror which is the quantum KodairaSpencer theory. The only degree of freedom of this theory is an unconventional chiral scalar on a Riemann surface. In this setup we identify the Bbranes on the mirror Riemann
Topological string theory on compact CalabiYau: Modularity and boundary conditions
, 2006
"... The topological string partition function Z(λ,t, ¯t) = exp(λ 2g−2 Fg(t, ¯t)) is calculated on a compact CalabiYau M. The Fg(t, ¯t) fulfill the holomorphic anomaly equations, which imply that Ψ = Z transforms as a wave function on the symplectic space H 3 (M, Z). This defines it everywhere in the m ..."
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Cited by 83 (11 self)
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The topological string partition function Z(λ,t, ¯t) = exp(λ 2g−2 Fg(t, ¯t)) is calculated on a compact CalabiYau M. The Fg(t, ¯t) fulfill the holomorphic anomaly equations, which imply that Ψ = Z transforms as a wave function on the symplectic space H 3 (M, Z). This defines it everywhere in the moduli space M(M) along with preferred local coordinates. Modular properties of the sections Fg as well as local constraints from the 4d effective action allow us to fix Z to a large extent. Currently with a newly found gap condition at the conifold, regularity at the orbifold and the most naive bounds from Castelnuovo’s theory, we can provide the boundary data, which specify Z, e.g. up to genus 51 for the quintic.
Exact and Asymptotic Degeneracies of Small Black Holes
, 2005
"... We examine the recently proposed relations between black hole entropy and the topological string in the context of type II/heterotic string dual models. We consider the degeneracies of perturbative heterotic BPS states. In several examples with N = 4 and N = 2 supersymmetry, we show that the macrosc ..."
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Cited by 80 (12 self)
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We examine the recently proposed relations between black hole entropy and the topological string in the context of type II/heterotic string dual models. We consider the degeneracies of perturbative heterotic BPS states. In several examples with N = 4 and N = 2 supersymmetry, we show that the macroscopic degeneracy of small black holes agrees to all orders with the microscopic degeneracy, but misses nonperturbative corrections which are computable in the heterotic dual. Using these examples we refine the previous proposals and comment on their domain of validity as well as on the relevance of helicity supertraces.
Threedimensional quantum gravity, ChernSimons theory, and the Apolynomial
, 2003
"... We study threedimensional ChernSimons theory with complex gauge group SL(2,C), which has many interesting connections with threedimensional quantum gravity and geometry of hyperbolic 3manifolds. We show that, in the presence of a single knotted Wilson loop in an infinitedimensional representati ..."
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Cited by 79 (11 self)
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We study threedimensional ChernSimons theory with complex gauge group SL(2,C), which has many interesting connections with threedimensional quantum gravity and geometry of hyperbolic 3manifolds. We show that, in the presence of a single knotted Wilson loop in an infinitedimensional representation of the gauge group, the classical and quantum properties of such theory are described by an algebraic curve called the Apolynomial of a knot. Using this approach, we find some new and rather surprising relations between the Apolynomial, the colored Jones polynomial, and other invariants of hyperbolic 3manifolds. These relations generalize the volume conjecture and the MelvinMortonRozansky conjecture, and suggest an intriguing connection between the SL(2,C) partition function and the colored Jones polynomial.
Topological Mtheory as Unification of Form Theories of Gravity
, 2004
"... We introduce a notion of topological Mtheory and argue that it provides a unification of form theories of gravity in various dimensions. Its classical solutions involve G2 holonomy metrics on 7manifolds, obtained from a topological action for a 3form gauge field introduced by Hitchin. We show tha ..."
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Cited by 70 (6 self)
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We introduce a notion of topological Mtheory and argue that it provides a unification of form theories of gravity in various dimensions. Its classical solutions involve G2 holonomy metrics on 7manifolds, obtained from a topological action for a 3form gauge field introduced by Hitchin. We show that by reductions of this 7dimensional theory one can classically obtain 6dimensional topological A and B models, the topological sector of loop quantum gravity in 4 dimensions, and ChernSimons gravity in 3 dimensions. We also find that the 7dimensional Mtheory perspective sheds some light on the fact that the topological string partition function is a wavefunction, as well as on Sduality between the A and B models. The degrees of freedom of the A and B models appear as conjugate variables in the 7dimensional theory. Finally, from the topological Mtheory perspective we find hints of an intriguing holographic link between nonsupersymmetric YangMills in