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269
Hierarchies from Fluxes in String Compactifications
, 2002
"... Warped compactifications with significant warping provide one of the few known mechanisms for naturally generating large hierarchies of physical scales. We demonstrate that this mechanism is realizable in string theory, and give examples involving orientifold compactifications of IIB string theory a ..."
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Cited by 715 (33 self)
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Warped compactifications with significant warping provide one of the few known mechanisms for naturally generating large hierarchies of physical scales. We demonstrate that this mechanism is realizable in string theory, and give examples involving orientifold compactifications of IIB string theory and Ftheory compactifications on CalabiYau fourfolds. In each case, the hierarchy of scales is fixed by a choice of RR and NS fluxes in the compact manifold. Our solutions involve compactifications of the KlebanovStrassler gravity dual to a confining N = 1 supersymmetric gauge theory, and the hierarchy reflects the small scale of chiral symmetry breaking in the dual gauge theory.
Fivebranes, Membranes And NonPerturbative String Theory
, 1995
"... Nonperturbative instanton corrections to the moduli space geometry of type IIA string theory compactified on a CalabiYau space are derived and found to contain order e \Gamma1=g s contributions, where g s is the string coupling. The computation reduces to a weighted sum of supersymmetric extrema ..."
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Cited by 387 (6 self)
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Nonperturbative instanton corrections to the moduli space geometry of type IIA string theory compactified on a CalabiYau space are derived and found to contain order e \Gamma1=g s contributions, where g s is the string coupling. The computation reduces to a weighted sum of supersymmetric extremal maps of strings, membranes and fivebranes into the CalabiYau space, all three of which enter on equal footing. It is shown that a supersymmetric 3cycle is one for which the pullback of the Kahler form vanishes and the pullback of the holomorphic threeform is a constant multiple of the volume element. Quantum mirror symmetry relates the sum in the IIA theory over supersymmetric, odddimensional cycles in the CalabiYau space to a sum in the IIB theory over supersymmetric, evendimensional cycles in the mirror.
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 → ∞.
Supergravity flows and Dbrane stability
, 2000
"... We investigate the correspondence between existence/stability of BPS states in type II string theory compactified on a CalabiYau manifold and BPS solutions of four dimensional N=2 supergravity. Some paradoxes emerge, and we propose a resolution by considering composite configurations. This in turn ..."
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Cited by 207 (14 self)
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We investigate the correspondence between existence/stability of BPS states in type II string theory compactified on a CalabiYau manifold and BPS solutions of four dimensional N=2 supergravity. Some paradoxes emerge, and we propose a resolution by considering composite configurations. This in turn gives a smooth effective field theory description of decay at marginal stability. We also discuss the connection with 3pronged strings, the Joyce transition of special Lagrangian submanifolds,
Mirror Symmetry is TDuality
, 1996
"... It is argued that every CalabiYau manifold X with a mirror Y admits a family of supersymmetric toroidal 3cycles. Moreover the moduli space of such cycles together with their flat connections is precisely the space Y . The mirror transformation is equivalent to Tduality on the 3cycles. The geomet ..."
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Cited by 182 (10 self)
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It is argued that every CalabiYau manifold X with a mirror Y admits a family of supersymmetric toroidal 3cycles. Moreover the moduli space of such cycles together with their flat connections is precisely the space Y . The mirror transformation is equivalent to Tduality on the 3cycles. The geometry of moduli space is addressed in a general framework. Several examples are discussed. y email: andy@denali.physics.ucsb.edu yy email: yau@abel.math.harvard.edu yyy email: zaslow@abel.math.harvard.edu 1. Introduction The discovery of mirror symmetry in string theory [1] has led to a number of mathematical surprises. Most investigations have focused on the implications of mirror symmetry of the geometry of CalabiYau moduli spaces. In this paper we shall consider the implications of mirror symmetry of the spectrum of BPS soliton states, which are associated to minimal cycles in the CalabiYau. New surprises will be found. The basic idea we will investigate is briefly as follows. Cons...
Black Hole Condensation And The Unification Of String Vacua
, 1995
"... It is argued that black hole condensation can occur at conifold singularities in the moduli space of type II CalabiYau string vacua. The condensate signals a smooth transition to a new CalabiYau space with different Euler characteristic and Hodge numbers. In this manner string theory unifies the m ..."
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Cited by 162 (14 self)
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It is argued that black hole condensation can occur at conifold singularities in the moduli space of type II CalabiYau string vacua. The condensate signals a smooth transition to a new CalabiYau space with different Euler characteristic and Hodge numbers. In this manner string theory unifies the moduli spaces of many or possibly all CalabiYau vacua. Elementary string states and black holes are smoothly interchanged under the transitions, and therefore cannot be invariantly distinguished. Furthermore, the transitions establish the existence of mirror symmetry for many or possibly all CalabiYau manifolds.
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.
Lectures on Dbranes
, 1998
"... This is an introduction to the physics of Dbranes. Topics covered include Polchinski’s original calculation, a critical assessment of some duality checks, Dbrane scattering, and effective worldvolume actions. Based on lectures given in 1997 at the Isaac Newton ..."
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Cited by 69 (5 self)
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This is an introduction to the physics of Dbranes. Topics covered include Polchinski’s original calculation, a critical assessment of some duality checks, Dbrane scattering, and effective worldvolume actions. Based on lectures given in 1997 at the Isaac Newton
Beauty is attractive: Moduli trapping at enhanced symmetry points,” JHEP 0405, 030 (2004) [arXiv:hepth/0403001]; T. Mohaupt and F. Saueressig, “Effective supergravity actions for conifold transitions
 JCAP
, 2004
"... We study quantum effects on moduli dynamics arising from the production of particles which are light at points of enhanced symmetry in moduli space. The resulting forces trap the moduli at these points. Moduli trapping occurs in timedependent quantum field theory, as well as in systems of moving D ..."
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Cited by 63 (13 self)
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We study quantum effects on moduli dynamics arising from the production of particles which are light at points of enhanced symmetry in moduli space. The resulting forces trap the moduli at these points. Moduli trapping occurs in timedependent quantum field theory, as well as in systems of moving Dbranes, where it leads the branes to combine into stacks. Trapping also occurs in the presence of gravity, though the range over which the moduli can roll is limited by Hubble friction. We observe that a scalar field trapped on a steep potential can induce a stage of acceleration of the universe, which we call trapped inflation. Moduli trapping ameliorates the cosmological moduli problem and may affect vacuum selection. In particular, rolling moduli are most powerfully attracted to the points of greatest symmetry. Given suitable assumptions about the dynamics of the very early universe, this effect might help to explain why among the plethora of possible vacuum states of string theory, we appear to live in one with a large number of (spontaneously