Calculations for mirror symmetry with D-branes

Walcher, Johannes

doi:10.1088/1126-6708/2009/09/129

Cited by 29 publications

(95 citation statements)

References 50 publications

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“…The on-shell results of one-deformation modulus compact CICYs with D-branes are agree with those in the papers 25,38 obtained from the direct integration method. We further compute the off-shell superpotentials of these models.…”

Section: Superpotentials and Ooguri-vafa Invariantssupporting

confidence: 87%

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Effective superpotentials of Type II D-brane/F-theory on compact complete intersection Calabi–Yau threefolds

Zou

Yang

2016

Mod. Phys. Lett. A

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In this paper, we extend the GKZ-system method to the more general case: compact Complete Intersection Calabi-Yau manifolds (CICY). For several one-deformation modulus compact CICYs with D-branes, the on-shell superpotentials in this paper from the extended GKZ-system method are exactly consistent with published results obtained from other methods. We further compute the off-shell superpotentials of these models. Then we obtain both the on-shell and off-shell superpotentials for several two-deformation moduli compact CICYs with D-branes by using the extended GKZ-system method. The discrete symmetrical groups, Z 2 , Z 3 and Z 4 , of the holomorphic curves wrapped by D-branes play the important roles in computing the superpotentials, in some sense, they are the quantum symmetries of these models.Furthermore, through the mirror symmetry, the Ooguri-Vafa invariants are extracted from the A-model instanton expansion.

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Section: Superpotentials and Ooguri-vafa Invariantssupporting

confidence: 87%

“…It's easy to see that results in paper 25 are agree with ours up to a linear combination. Let c ′ 1 = −2, and the mirror map is also given by Eq.(62).…”

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confidence: 84%

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Effective superpotentials of Type II D-brane/F-theory on compact complete intersection Calabi–Yau threefolds

Zou

Yang

2016

Mod. Phys. Lett. A

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“…We consider explicitly the P 5 [3,3] case following the analysis in [47]. This corresponds to the complete intersection Calabi-Yau (see, for example, [48] for a discussion)…”

Section: IImentioning

confidence: 99%

Infinite distances in field space and massless towers of states

Grimm

Palti

Valenzuela

2018

J. High Energ. Phys.

290

728

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It has been conjectured that in theories consistent with quantum gravity infinite distances in field space coincide with an infinite tower of states becoming massless exponentially fast in the proper field distance. The complex-structure moduli space of Calabi-Yau manifolds is a good testing ground for this conjecture since it is known to encode quantum gravity physics. We study infinite distances in this setting and present new evidence for the above conjecture. Points in moduli space which are at infinite proper distance along any path are characterised by an infinite order monodromy matrix. We utilise the nilpotent orbit theorem to show that for a large class of such points the monodromy matrix generates an infinite orbit within the spectrum of BPS states. We identify an infinite tower of states with this orbit. Further, the theorem gives the local metric on the moduli space which can be used to show that the mass of the states decreases exponentially fast upon approaching the point. We also propose a reason for why infinite distances are related to infinite towers of states. Specifically, we present evidence that the infinite distance itself is an emergent quantum phenomenon induced by integrating out at one-loop the states that become massless. Concretely, we show that the behaviour of the field space metric upon approaching infinite distance can be recovered from integrating out the BPS states. Similarly, at infinite distance the gauge couplings of closed-string Abelian gauge symmetries vanish in a way which can be matched onto integrating out the infinite tower of charged BPS states. This presents evidence towards the idea that also the gauge theory weak-coupling limit can be thought of as emergent.

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“…It was first proposed and demonstrated for non-compact toric Calabi-Yau threefolds in [109][110][111]268] to use open-closed Picard-Fuchs systems to obtain the brane superpotential. For D5-branes in compact geometries the superpotential was calculated in [112,114,[116][117][118]122] by deriving and solving inhomogeneous Picard-Fuchs equations. Finally the methods of [110,111] have been extended to compact geometries in [115] and further applied in [120,121,[123][124][125][126][127][128][129].…”

Section: Chaptermentioning

confidence: 99%

Holomorphic couplings in non‐perturbative string compactifications

Klevers

2011

Fortschritte der Physik

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In this review article 1 we present an analysis of several aspects of four-dimensional, nonperturbative N = 1 compactifications of string theory. Our study focuses on brane dynamics and their effective physics as encoded in the holomorphic couplings of the low-energy N = 1 effective action, most prominently the superpotential W . This article is divided into three parts. In part one we derive the effective action of a spacetime-filling D5-brane in generic Type IIB Calabi-Yau orientifold compactifications. In the second part we invoke tools from string dualities, namely from F-theory, heterotic/F-theory duality and mirror symmetry, for a more elaborate study of the dynamics of (p, q) 7-branes and heterotic five-branes. In this context we perform exact computations of the complete perturbative effective superpotential, both due to branes and background fluxes. Finally, in the third part we present a novel geometric description of five-branes in Type IIB and heterotic M-theory Calabi-Yau compactifications via a non-Calabi-Yau threefoldẐ 3 , that is canonically constructed from the original fivebrane and the Calabi-Yau threefold Z 3 via a blow-up. We use the blow-up threefoldẐ 3 to derive open-closed Picard-Fuchs differential equations, that govern the complete effective brane and flux superpotential. In addition, we present first evidence to interpretẐ 3 as a flux compactification geometrically dual to the original five-brane by defining an SU (3)-structure onẐ 3 , that is generated dynamically by the five-brane backreaction.

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Calculations for mirror symmetry with D-branes

Cited by 29 publications

References 50 publications

Effective superpotentials of Type II D-brane/F-theory on compact complete intersection Calabi–Yau threefolds

Effective superpotentials of Type II D-brane/F-theory on compact complete intersection Calabi–Yau threefolds

Infinite distances in field space and massless towers of states

Holomorphic couplings in non‐perturbative string compactifications

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