F Theory Vacua in Four Dimensions and Toric Threefolds

Mohri, Kenji

doi:10.1142/s0217751x99000415

Cited by 30 publications

(88 citation statements)

References 39 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…In the higherdimensional fibration, the coefficients of the polynomials in p will become functions of the variables of the base B n -i. More precisely, (y, rr, i, v) become 9 Toric constructions of Calabi-Yau 4-folds have been discussed in [45,46,47,48,49].…”

Section: Description Of the Bundlementioning

confidence: 99%

See 1 more Smart Citation

Heterotic string/F-theory duality from mirror symmetry

Berglund¹,

Mayr²

1998

Advances in Theoretical and Mathematical Physics

187

View full text Add to dashboard Cite

We use local mirror symmetry in type IIA string compactifications on Calabi-Yau n -f 1 folds X n+ i to construct vector bundles on (possibly singular) elliptically fibered Calabi-Yau n-folds Z n . The interpretation of these data as valid classical solutions of the heterotic string compactified on Z n proves F-theory/heterotic duality at the classical level. Toric geometry is used to establish a systematic dictionary that assigns to each given toric n + 1-fold X n +i a toric n fold Z n together with a specific family of sheaves on it. This allows for a systematic construction of phenomenologically interesting d = 4 N = 1 heterotic vacua, e.g. on deformations of the tangent bundle, with grand unified and 5(7(3) x 5(7(2) gauge groups. As another application we find non-perturbative gauge enhancements of the heterotic string on singular Calabi-Yau manifolds and new non-perturbative dualities relating heterotic compactifications on different manifolds.e-print

show abstract

Section: Description Of the Bundlementioning

confidence: 99%

“…This can be argued from considering a compactification on S 1 and comparison with M-theory, which leads to the following contribution of the hodge numbers of W4 to the four-dimensional fields [48] 24…”

Section: Non-perturbative Gauge Symmetries From Non-toric Basesmentioning

confidence: 99%

Heterotic string/F-theory duality from mirror symmetry

Berglund¹,

Mayr²

1998

Advances in Theoretical and Mathematical Physics

187

View full text Add to dashboard Cite

show abstract

“…Again we refer to the literature for a more detailed analysis of the four-dimensional N = 1 spectrum and the translation to the heterotic side, see [183,[222][223][224] and [217] for a detailed derivation of the F-theory effective action in a dimensional reduction on X 4 . Upon a further compactification on T 2 heterotic/F-theory duality becomes heterotic/Type II duality in two dimensions which can alternatively be used for an discussion of the massless spectrum and effective action [151,225].…”

Section: Heterotic/f-theory Duality In Lower Dimensionsmentioning

confidence: 99%

Holomorphic couplings in non‐perturbative string compactifications

Klevers

2011

Fortschritte der Physik

View full text Add to dashboard Cite

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.

show abstract

“…18 of them are toric threefolds p n (1 n 18) and are completely classified [83,84,85,86]. They were studied in the context of Calabi-Yau fourfold compactifications over Fano threefolds [44,79]. In particular in [82], it was shown that for k 0Y XXXY 6 over B 3 k there exists a smooth Weierstrass model (having a section); B 3 k with k 0Y 1Y 2Y 3 correspond to the toric Fano three-folds p n with n 2Y 9Y 13Y 17.…”

Section: 1mentioning

confidence: 99%

“…One finds In the following we restrict to k 0Y 1Y 2Y 3 where one has h 21 0, [44,79], h 11 X 4 k 3 k, h 31 X 4 k c 6 À 8 À 3 k 28 3619 À k [44,79,25]. Now since we have a smooth Weierstrass model and thus expecting no unbroken gauge group, i.e.…”

Section: 1mentioning

confidence: 99%

Untitled

Andreas

1999

Fortschr. Phys.

View full text Add to dashboard Cite

We review aspects of N = 1 duality between the heterotic string and F‐theory. After a description of string duality intended for the non‐specialist the framework and the constraints for heterotic/F‐theory compactifications are presented. The computations of the necessary Calabi‐Yau manifold and vector bundle data, involving characteristic classes and bundle moduli, are given in detail. The matching of the spectrum of chiral multiplets and of the number of heterotic five‐branes respectively F‐theory three‐branes, needed for anomaly cancellation in four‐dimensional vacua, is pointed out. Several examples of four‐dimensional dual pairs are constructed where on both sides the geometry of the involved manifolds relies on del Pezzo surfaces.

show abstract

F Theory Vacua in Four Dimensions and Toric Threefolds

Abstract: We investigate D=4, N=1 F theory models realized by type IIB string compactification on toric threefolds. Massless spectra, gauge symmetries, phase transitions associated with divisor contractions and flops, and non-perturbative superpotentials are analyzed using elementary toric methods.

Cited by 30 publications

References 39 publications

Heterotic string/F-theory duality from mirror symmetry

Heterotic string/F-theory duality from mirror symmetry

Holomorphic couplings in non‐perturbative string compactifications

Untitled

Contact Info

Product

Resources

About