Mirror symmetry and the moduli space for generic hypersurfaces in toric varieties

Berglund, Per; Katz, Sheldon; Klemm, Albrecht

doi:10.1016/0550-3213(95)00434-2

Cited by 63 publications

(123 citation statements)

References 59 publications

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“…(2.21) constrains the dilaton dependent shifts of all variables. * The same phenomenon has been observed by Berglund, Katz, Klemm and Mayr [44] and we are grateful for communication of these results prior to publication.…”

Section: Construction Of Calabi-yau Manifolds Using Toric Geometrysupporting

confidence: 87%

Non-perturbative properties of heterotic string vacua compactified on K3 × T2

Louis¹,

Sonnenschein

Theisen³

et al. 1996

Nuclear Physics B

116

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Using the heterotic-type II duality of N = 2 string vacua in four space-time dimensions we study non-perturbative couplings of toroidally compactified six-dimensional heterotic vacua. In particular, the heteroticheterotic S-duality and the Coulomb branch of tensor multiplets observed in six dimensions are studied from a four-dimensional point of view. We explicitly compute the couplings of the vector multiplets of several type II vacua and investigate the implications for their heterotic duals.

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Section: Construction Of Calabi-yau Manifolds Using Toric Geometrysupporting

confidence: 87%

Non-perturbative properties of heterotic string vacua compactified on K3 × T2

Louis¹,

Sonnenschein

Theisen³

et al. 1996

Nuclear Physics B

116

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“…Since this cone is identical to the cone generated by the curves coming from intersections of the hypersurface equation with two toric divisors, we conclude that (3.8) and (3.9) span indeed the Kähler cone of the CY hypersurface [36].…”

Section: Jhep05(2014)001mentioning

confidence: 73%

Explicit de Sitter flux vacua for global string models with chiral matter

Cicoli

Klevers

Krippendorf³

et al. 2014

J. High Energ. Phys.

140

222

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Abstract:We address the open question of performing an explicit stabilisation of all closed string moduli (including dilaton, complex structure and Kähler moduli) in fluxed type IIB Calabi-Yau compactifications with chiral matter. Using toric geometry we construct Calabi-Yau manifolds with del Pezzo singularities. D-branes located at such singularities can support the Standard Model gauge group and matter content or some close extensions. In order to control complex structure moduli stabilisation we consider CalabiYau manifolds which exhibit a discrete symmetry that reduces the effective number of complex structure moduli. We calculate the corresponding periods in the symplectic basis of invariant three-cycles and find explicit flux vacua for concrete examples. We compute the values of the flux superpotential and the string coupling at these vacua. Starting from these explicit complex structure solutions, we obtain AdS and dS minima where the Kähler moduli are stabilised by a mixture of D-terms, non-perturbative and perturbative α ′ corrections as in the LARGE Volume Scenario. In the considered example the visible sector lives at a dP 6 singularity which can be higgsed to the phenomenologically interesting class of models at the dP 3 singularity.

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“…Topologically it is not difficult to observe that U is an R 4 -bundle over P 1 C . In fact by splitting z j in real and imaginary parts, equations (12) give rise to 4 linear equations in R 8 parameterized by [y 0 , y 1 ] ∈ P 1 C . To construct the diffeomorphism introduce the coordinates change given by (8) and split the new coordinates in real and imaginary parts:…”

Section: 1mentioning

confidence: 99%

“…a geometric transition whose associated birational contraction generates at most ordinary double points. After this pivotal paper other geometric transitions have been physically understood [12], [41], [13]. For many geometric transitions, the induced change in topology can be summarized by saying that a transition increases complex moduli and decreases Kähler moduli.…”

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confidence: 99%