Matrix models, 4D black holes and topological strings on non-compact Calabi-Yau manifolds

Danielsson, Ulf H.; Olsson, Martin E.; Vonk, Marcel

doi:10.1088/1126-6708/2004/11/007

Cited by 13 publications

(40 citation statements)

References 34 publications

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“…The fiber st = const is a cylinder, except over the loci uv + (µ ± iq) = 0, where it is the intersection of two complex planes in a single point. As is well-known (see the appendix of [10] for a pictorial explanation) the complex structure moduli of the manifold are related to A-cycles which are localized near these loci, and B-cycles which start there and run off to infinity. Since for q large these loci are far away from each other, the geometry of Eq.…”

Section: The 0a Matrix Model At Self-dual Radiusmentioning

confidence: 89%

“…This corresponds to the 0B matrix model, which also is non-perturbatively stable. The 0A and 0B matrix models were constructed in [11,12], and their relations at different radii were discussed in detail in [10], to which we refer for further reading.…”

Section: The Geometry Of the 0a Matrix Modelmentioning

confidence: 99%

“…However, it will be important when we construct the geometries, and natural later on when we are matching variables. Moreover, it will matter for the nonperturbative part of the theory [10].…”

Section: The Geometry Of the 0a Matrix Modelmentioning

confidence: 99%

“…It has been proposed [5,10] that the ground ring equation for the 0A model at self-dual radius including both its deformations is…”

Section: The 0a Matrix Model At Self-dual Radiusmentioning

confidence: 99%

“…[33]. In [10,34], two different ways to deal with the truly noncompact case by introducing cutoffs were discussed.…”

Section: Black Hole Entropy and Compact Calabi-yausmentioning

confidence: 99%

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4D black holes and holomorphic factorization of the 0A matrix model

Danielsson¹,

Johansson²,

Larfors³

et al. 2005

J. High Energy Phys.

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In this letter, we relate the free energy of the 0A matrix model to the sum of topological and anti-topological string amplitudes. For arbitrary integer multiples of the matrix model self-dual radius we describe the geometry on which the corresponding topological string propagates. This geometry is not the one that follows from the usual ground ring analysis, but in a sense its "holomorphic square root". Mixing of terms for different genus in the matrix model free energy yields one-loop terms compatible with type II strings on compact Calabi-Yau target spaces. As an application, we give an explicit example of how to relate the 0A matrix model free energy to that of a four-dimensional black hole in type IIB theory, compactified on a compact Calabi-Yau. Variables, Legendre transforms, and large classical terms on both sides match perfectly.

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Section: The 0a Matrix Model At Self-dual Radiusmentioning

confidence: 89%

Section: The Geometry Of the 0a Matrix Modelmentioning

confidence: 99%

Section: The Geometry Of the 0a Matrix Modelmentioning

confidence: 99%

“…It has been proposed [5,10] that the ground ring equation for the 0A model at self-dual radius including both its deformations is…”

Section: The 0a Matrix Model At Self-dual Radiusmentioning

confidence: 99%

“…[33]. In [10,34], two different ways to deal with the truly noncompact case by introducing cutoffs were discussed.…”

Section: Black Hole Entropy and Compact Calabi-yausmentioning

confidence: 99%

See 3 more Smart Citations

4D black holes and holomorphic factorization of the 0A matrix model

Danielsson¹,

Johansson²,

Larfors³

et al. 2005

J. High Energy Phys.

Self Cite

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Topological B-model and cˆ=1 string theory

Hyun

Park

et al. 2005

Nuclear Physics B

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We study the topological B-model on a deformed Z 2 orbifolded conifold by investigating variation of complex structures via quantum Kodaira-Spencer theories. The fermionic/brane formulation together with systematic utilization of symmetries of the geometry gives rise to a free fermion realization of the amplitudes. We derive Ward identities which solve the perturbed free energy exactly. We also obtain the corresponding Kontsevich-like matrix model. All these confirm the recent conjecture on the connection of the theory withĉ = 1 type 0A string theory compactified at the radius R = α ′ /2.

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Thermodynamics of noncritical M-theory and the topological A-model

Hořava

Keeler

2006

Nuclear Physics B

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In hep-th/0508024, noncritical M-theory for two-dimensional Type 0A and 0B strings was defined in terms of a double-scaled theory of nonrelativistic fermions in 2 + 1 dimensions. Here we study this noncritical M-theory at finite temperature. We derive the exact expression for the free energy of its vacuum solution, as a function of a coupling constant g M and the radius R of the thermal circle. We show that at high temperature, the theory is effectively described by another M-theory solution, whose effective loop-counting coupling scales in a novel way characteristic of M-theory, as T 3 . Our calculations further suggest that noncritical M-theory is dual to the closed string theory of the topological A-model on a Calabi-Yau, with the radius R of the Euclidean time circle in M-theory playing the role of the string coupling constant of the A-model. In this correspondence, T-duality on the Euclidean time circle of noncritical M-theory implies an S-duality for the topological A-model. December 2005

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Matrix models, 4D black holes and topological strings on non-compact Calabi-Yau manifolds

Cited by 13 publications

References 34 publications

4D black holes and holomorphic factorization of the 0A matrix model

4D black holes and holomorphic factorization of the 0A matrix model

Topological B-model and cˆ=1 string theory

Thermodynamics of noncritical M-theory and the topological A-model

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