c = 1 string as the topological theory of the conifold

Ghoshal, Debashis; Vafa, Cumrun

doi:10.1016/0550-3213(95)00408-k

Cited by 181 publications

(334 citation statements)

References 33 publications

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“…Therefore, the type 0 matrix models are, in terms of the partition functions, the square of the bosonic one. From [3] we have, Z bosonic = Z top , suggesting Z 0A/0B = |Z top | 2 . Admittedly, this reasonling is somewhat speculative.…”

Section: Black Hole Physics From Matrix Models 21 Black Hole Entropymentioning

confidence: 94%

“…As we explained, the grand canonical free energy of the matrix model should be the same as the one for the black hole, thus allowing us to make the identification 3 Z…”

Section: Black Hole Physics From Matrix Models 21 Black Hole Entropymentioning

confidence: 99%

“…It has, however, also been known for a long time that the bosonic c = 1 matrix model, at the self-dual radius, arises in a completely different context, namely in relation to topological string theory on the deformed conifold [3]. In fact, it is now known that there are very general relations between topological string theories and matrix models, see for example [4].…”

Section: Introductionmentioning

confidence: 99%

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

Danielsson¹,

Olsson²,

Vonk³

2004

J. High Energy Phys.

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We study the relation between c = 1 matrix models at self-dual radii and topological strings on non-compact Calabi-Yau manifolds. Particularly the special case of the deformed matrix model is investigated in detail. Using recent results on the equivalence of the partition function of topological strings and that of four dimensional BPS black holes, we are able to calculate the entropy of the black holes, using matrix models. In particular, we show how to deal with the divergences that arise as a result of the non-compactness of the Calabi-Yau. The main result is that the entropy of the black hole at zero temperature coincides with the canonical free energy of the matrix model, up to a proportionality constant given by the self-dual temperature of the matrix model.

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Section: Black Hole Physics From Matrix Models 21 Black Hole Entropymentioning

confidence: 94%

“…As we explained, the grand canonical free energy of the matrix model should be the same as the one for the black hole, thus allowing us to make the identification 3 Z…”

Section: Black Hole Physics From Matrix Models 21 Black Hole Entropymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Danielsson¹,

Olsson²,

Vonk³

2004

J. High Energy Phys.

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show abstract

“…Since this SCFT is relevant for both the deformed conifold and the ALE space [36,12,9,13,37], such a study should improve our understanding of D-…”

Section: Jhep08(2001)045mentioning

confidence: 99%

Duality of the fermionic 2d black hole and N = 2 Liouville theory as mirror symmetry

Hori

Kapustin

2001

J. High Energy Phys.

216

428

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Abstract:We prove the equivalence of the SL(2, R)/ U(1) Kazama-Suzuki model, which is a fermionic generalization of the 2d Black Hole, and N = 2 Liouville theory. We show that this duality is an example of mirror symmetry. The essential part of the derivation is to realize the fermionic 2d Black Hole as the low energy limit of a gauged linear sigma-model. Liouville theory is obtained by dualizing the charged scalar fields and taking into account the vortex-instanton effects, as proposed recently in non-dilatonic models. The gauged linear sigma-model we study has many useful generalizations which we briefly discuss. In particular, we show how to construct a variety of dilatonic superstring backgrounds which generalize the fermionic 2d Black Hole and admit a mirror description in terms of Toda-like theories.

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“…As for other topological string models, the free energies F g of X p exhibit singular behavior for p > 2 at a particular point t c = 0 in the Kähler moduli space. For most topological string models, this point is the conifold point and the singular behavior is described by the c = 1 string at self-dual radius [17]. In the case of topological string theory on local curves, however, the singular behavior is described by the c = 0 string, i.e.…”

Section: Introductionmentioning

confidence: 99%

Topological Strings on Local Curves

Mariño

2009

New Trends in Mathematical Physics

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We review some perturbative and nonperturbative aspects of topological string theory on the Calabi-Yau manifolds X p = O(−p) ⊕ O(p − 2) → P 1 . These are exactly solvable models of topological string theory which exhibit a nontrivial yet simple phase structure, and have a phase transition in the universality class of pure two-dimensional gravity. They don't have conventional mirror description, but a mirror B model can be formulated in terms of recursion relations on a spectral curve typical of matrix model theory. This makes it possible to calculate nonperturbative, spacetime instanton effects in a reliable way, and in particular to characterize the large order behavior of string perturbation theory.

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c = 1 string as the topological theory of the conifold

Cited by 181 publications

References 33 publications

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

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

Duality of the fermionic 2d black hole and N = 2 Liouville theory as mirror symmetry

Topological Strings on Local Curves

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