Mirror symmetry and a<i>G</i><sub>2</sub>flop

Aganagic, Mina; Vafa, Cumrun

doi:10.1088/1126-6708/2003/05/061

Cited by 34 publications

(53 citation statements)

References 32 publications

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“…Therefore the M theory duality implies the Chern-Simons/topological closed string duality. Various aspects of the lifting of type IIA configurations to G 2 holonomy manifolds have been studied in a number of papers [16,17,18].…”

Section: Large N Chern-simons Dualitymentioning

confidence: 99%

“…If r = 0, solutions to V = 0 are given by σ = 0 and a i , b i obeying the constraint 17) modulo the gauge symmetry…”

Section: Linear Sigma-model Description Of the Worldsheetmentioning

confidence: 99%

“…The topological string amplitudes at g = 0 and 1 are somewhat special. For g = 0, we have 17) where Q(t) is a quadratic polynomial in t. The easiest way to see that is to note that ∂F (C) 0,0 /∂t is a period integral given by…”

Section: Let Us Compute F (C)mentioning

confidence: 99%

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Worldsheet derivation of a large N duality

2002

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We give a worldsheet proof of the equivalence between the U (N ) Chern-Simons gauge theory on S 3 and the topological closed string theory on the resolved conifold geometry.When the 't Hooft coupling of the gauge theory is small, the dual closed string worldsheet develops a new branch. We show that the fluctuations of the worldsheet into this branch effectively correspond to "holes" on the worldsheet, generating an open string sector. This leads to a microscopic description of how the 't Hooft expansion of gauge theory amplitudes is reproduced in the closed string computation. We find that the closed string amplitudes also contain terms which are not captured in the 't Hooft expansion but are present in the exact computation in the gauge theory amplitudes. These arise when the whole Riemann surface is in the new branch. We also discuss the cases with SO and Sp gauge groups.

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Section: Large N Chern-simons Dualitymentioning

confidence: 99%

“…If r = 0, solutions to V = 0 are given by σ = 0 and a i , b i obeying the constraint 17) modulo the gauge symmetry…”

Section: Linear Sigma-model Description Of the Worldsheetmentioning

confidence: 99%

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Worldsheet derivation of a large N duality

2002

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“…This is the route found in [32] and the technique is further developed in [24] on which the present computation is based. The Type IIB dual is the non-compact Calabi-Yau (ξ, η ∈ C; x, y ∈ C × ) This is what we call the g = 1 branch.…”

Section: N =mentioning

confidence: 96%

Non-perturbative orientifold transitions at the conifold

Hori

Hosomichi

Page

et al. 2005

J. High Energy Phys.

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After orientifold projection, the conifold singularity in hypermultiplet moduli space of Calabi-Yau compactifications cannot be avoided by geometric deformations. We study the non-perturbative fate of this singularity in a local model involving O6-planes and D6-branes wrapping the deformed conifold in Type IIA string theory. We classify possible A-type orientifolds of the deformed conifold and find that they cannot all be continued to the small resolution. When passing through the singularity on the deformed side, the O-plane charge generally jumps by the class of the vanishing cycle. To decide which classical configurations are dynamically connected, we construct the quantum moduli space by lifting the orientifold to M-theory as well as by looking at the superpotential. We find a rich pattern of smooth and phase transitions depending on the total sixbrane charge. Non-BPS states from branes wrapped on nonsupersymmetric bolts are responsible for a phase transition. We also clarify the nature of a Z 2 valued D0-brane charge in the 6-brane background. Along the way, we obtain a new metric of G 2 holonomy corresponding to an O6-plane on the three sphere of the deformed conifold.June 2005

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“…These proceed via a phase transition but, unlike the conifold transition, do not appear to be related to condensation of any particle state 1 . For related work, see [8].…”

Section: Introductionmentioning

confidence: 99%

Conifold transitions and five-brane condensation in M-theory onSpin(7) manifolds

Gukov

Sparks

Tong

2003

Class. Quantum Grav.

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We conjecture a topology changing transition in M-theory on a non-compact asymptotically conical Spin(7) manifold, where a 5-sphere collapses and a CP 2 bolt grows. We argue that the transition may be understood as the condensation of M5-branes wrapping S 5 . Upon reduction to ten dimensions, it has a physical interpretation as a transition of D6-branes lying on calibrated submanifolds of flat space. In yet another guise, it may be seen as a geometric transition between two phases of type IIA string theory on a G 2 holonomy manifold with either wrapped D6-branes, or background Ramond-Ramond flux. This is the first nontrivial example of a topology changing transition with only 1/16 supersymmetry.

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Mirror symmetry and aG₂flop

Cited by 34 publications

References 32 publications

Worldsheet derivation of a large N duality

Worldsheet derivation of a large N duality

Non-perturbative orientifold transitions at the conifold

Conifold transitions and five-brane condensation in M-theory onSpin(7) manifolds

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Mirror symmetry and aG2flop

Cited by 34 publications

References 32 publications

Worldsheet derivation of a large N duality

Worldsheet derivation of a large N duality

Non-perturbative orientifold transitions at the conifold

Conifold transitions and five-brane condensation in M-theory onSpin(7) manifolds

Contact Info

Product

Resources

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Mirror symmetry and aG₂flop