Periods for Calabi-Yau and Landau-Ginzburg vacua

Berglund, Per; Candelas, Philip; Ossa, Xenia de la; Font, Anamarı́a; Hübsch, Tristan; Jancic, Dubravka; Quevedo, Fernando

doi:10.1016/0550-3213(94)90047-7

Cited by 82 publications

(186 citation statements)

References 37 publications

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“…The classical expansion coefficients are given by intersections of the mirror dual Calabi-Yau three-fold M d 3 [29][30][31] (see also [32]). For historical reasons, the coefficients κ ijk are called (the classical) Yukawa couplings [33].…”

Section: Jhep03(2016)064mentioning

confidence: 99%

Universal properties of type IIB and F-theory flux compactifications at large complex structure

Marsh¹,

Sousa²

2016

J. High Energ. Phys.

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Abstract:We consider flux compactifications of type IIB string theory and F-theory in which the respective superpotentials at large complex structure are dominated by cubic or quartic terms in the complex structure moduli. In this limit, the low-energy effective theory exhibits universal properties that are insensitive to the details of the compactification manifold or the flux configuration. Focussing on the complex structure and axio-dilaton sector, we show that there are no vacua in this region and the spectrum of the Hessian matrix is highly peaked and consists only of three distinct eigenvalues (0, 2m 2 3/2 and 8m 2 3/2 ), independently of the number of moduli. We briefly comment on how the inclusion of Kähler moduli affect these findings. Our results generalise those of Brodie & Marsh [1], in which these universal properties were found in a subspace of the large complex structure limit of type IIB compactifications.

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Section: Jhep03(2016)064mentioning

confidence: 99%

Universal properties of type IIB and F-theory flux compactifications at large complex structure

Marsh¹,

Sousa²

2016

J. High Energ. Phys.

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“…This is for instance the situation for the Tian-Yau manifold. If a Landau-Ginzburg prescription of the model is available, also those perturbations that are not of this kind, can be represented as roots of monomial deformations, as was suggested in [17].…”

Section: Introductionmentioning

confidence: 99%

Mirror symmetry, mirror map and applications to complete intersection Calabi-Yau spaces

et al. 1995

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Abstract:We extend the discussion of mirror symmetry, Picard-Fuchs equations, instanton-corrected Yukawa couplings, and the topological one-loop partition function to the case of complete intersections with higher-dimensional moduli spaces. We will develop a new method of obtaining the instanton-corrected Yukawa couplings through a study of the solutions of the Picard-Fuchs equations. This leads to closed formulas for the prepotential for the Kähler moduli fields induced from the ambient space for all complete intersections in non singular weighted projective spaces. As examples we treat part of the moduli space of the phenomenologically interesting three-generation models that are found in this class. We also apply our method to solve the simplest model in which a topology change was observed and discuss examples of complete intersections in singular ambient spaces.

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“…Let us consider now 15 The dependence of the Kähler potential on the complex structure moduli can be worked out by computing the different periods of the CY three-fold under consideration. As derived in [233], for the simplest example of a CY manifold with just one complex structure modulus Table 9.3: Lower bounds on the physical volume as seen by the string V s ∼ 10 x−3/2 for some benchmark scenarios. Now writing V ≃ 10 x , R becomes a function of x and c. Finally, we can make a 3D plot of R with c min < c < c max and 2 < x < 15, and see in which region R > 1.…”

Section: Lower Bound On the Volumementioning

confidence: 99%

String loop moduli stabilisation and cosmology in IIB flux compactifications

Cicoli¹

2010

Fortschritte der Physik

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We present a detailed review of the moduli stabilisation mechanism and possible cosmological implications of the LARGE Volume Scenario (LVS) that emerges naturally in the context of type IIB Calabi‐Yau flux compactifications. After a quick overview of physics beyond the Standard Model, we present string theory as the most promising candidate for a consistent theory of quantum gravity. We then give a pedagogical introduction to type IIB compactifications on Calabi‐Yau orientifolds where most of the moduli are stabilised by turning on background fluxes. However in order to fix the Kähler moduli one needs to consider several corrections beyond the leading order approximations. After presenting a survey of all the existing solutions to this problem, we derive the topological conditions on an arbitrary Calabi‐Yau to obtain the LVS since it requires no fine‐tuning of the fluxes and provides a natural solution of the hierarchy problem. After performing a systematic study of the behaviour of string loop corrections for general type IIB compactifications, we show how they play a crucial rôle to achieve full Kähler moduli stabilisation in the LVS. Before examining the possible cosmological implication of these scenarios, we present a broad overview of string cosmology. We then notice how, in the case of K3‐fibrations, string loop corrections give rise naturally to an inflationary model which yields observable gravity waves. We finally study the finite‐temperature behaviour of the LVS and discuss prospects for future work.

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Periods for Calabi-Yau and Landau-Ginzburg vacua

Cited by 82 publications

References 37 publications

Universal properties of type IIB and F-theory flux compactifications at large complex structure

Universal properties of type IIB and F-theory flux compactifications at large complex structure

Mirror symmetry, mirror map and applications to complete intersection Calabi-Yau spaces

String loop moduli stabilisation and cosmology in IIB flux compactifications

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