Three-branes and five-branes in N=1 dual string pairs

Andreas, Bjorn; Curio, Gottfried

doi:10.1016/s0370-2693(97)01342-7

Cited by 27 publications

(79 citation statements)

References 8 publications

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“…Type (b) intersection points are characterized by the intersection of the curve D and a locus of order-2 points, σ ′ . σ ′ (denoted by σ 2 in [18]) is topologically σ ′ ∼ 3σ − 3K B 2 [25]. Using the topological form of D in (80) for N = 3, we find that there are …”

Section: Rank-3 Vector Bundlesmentioning

confidence: 95%

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New aspects of Heterotic–F-theory duality

et al. 2009

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In order to understand both up-type and down-type Yukawa couplings, F-theory is a better framework than the perturbative Type IIB string theory. The duality between the Heterotic and F-theory is a powerful tool in gaining more insights into F-theory description of low-energy chiral multiplets. Because chiral multiplets from bundles ∧ 2 V and ∧ 2 V × as well as those from a bundle V are all involved in Yukawa couplings in Heterotic compactification, we need to translate descriptions of all those kinds of matter multiplets into F-theory language through the duality. We find that chiral matter multiplets in F-theory are global holomorphic sections of line bundles on what we call covering matter curves. The covering matter curves are formulated in Heterotic theory in association with normalization of spectral surface, while they are where M 2-branes wrapped on a vanishing two-cycle propagate in F-theory. Chirality formulae are given purely in terms of primitive four-form flux. In order to complete the translation, the dictionary of the Heterotic-F theory duality has to be refined in some aspects. A precise map of spectral surface and complex structure moduli is obtained, and with the map, we find that divisors specifying the line bundles correspond precisely to codimension-3 singularities in F-theory.

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Section: Rank-3 Vector Bundlesmentioning

confidence: 95%

“…Thus, the discussion around equations (22)(23)(24)(25)(26) is applied for the bundles ρ(V ) = ∧ 2 V and ∧ 2 V × as well. In particular, the sheaf on the matter curvec ∧ 2 V is given by…”

Section: Resolving Double-curve Singularity Ofmentioning

confidence: 99%

New aspects of Heterotic–F-theory duality

et al. 2009

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“…A consistent F-theory compactification on an Calabi-Yau fourfold Y 5 requires a number χ(Y )/24 of three-branes filling the transverse space time R 3,1 [31]. This number agrees with the number of five-branes required for consistent F-theory compactification giving a non-trivial test for the expected heterotic/F-theory duality [1,5] and the adiabatic argument.…”

Section: F-theory Perspectivementioning

confidence: 63%

“…Further one expects that in the transition extra chiral matter occurs (if the original bundle V had non zero c 3 (V )) [2] which is on the heterotic side related to the moduli we are aiming to evaluate. 5 here assumed to be elliptically fibered over a three dimensional base B which is a P 1 bundle over the same B2 as considered on the heterotic string side 6 [2] argues that a three-brane can only dissolve on a multiple seven-brane…”

Section: Such a Transition Leads To A Modification Of The Anomaly Canmentioning

confidence: 99%

“…It has been shown that these five-branes match precisely the number of space-time filling three-branes necessary for tadpole cancellation in F-theory compactified on elliptically fibered Calabi-Yau fourfolds Y [1]. Various aspects of the map between the geometrical moduli of the pair (X, V ) and those of Y have been studied in [1,2,3,4,5,6,7]. The question of which pairs (X, V ) are stable under world-sheet instanton corrections [8] has been recently reconsidered in [9,10].…”

Section: Introductionmentioning

confidence: 98%

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Comments on <i>N</i> = 1 Heterotic String Vacua

Andreas¹,

Ruipérez²

2003

Advances in Theoretical and Mathematical Physics

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We analyze three aspects of N = 1 heterotic string compactifications on elliptically fibered Calabi-Yau threefolds: stability of vector bundles, five-brane instanton transitions and chiral matter. First we show that relative Fourier-Mukai transformation preserves absolute stability. This is relevant for vector bundles whose spectral cover is reducible. Then we derive an explicit formula for the number of moduli which occur in (vertical) five-brane instanton transitions provided a certain vanishing argument applies. Such transitions increase the holonomy of the heterotic vector bundle and cause gauge changing phase transitions. In a M-theory description the transitions are associated with collisions of bulk five-branes with one of the boundary fixed planes. In F-theory they correspond to three-brane instanton transitions. Our derivation relies on an index computation with data localized along the curve which is related to the existence of chiral matter in this class of heterotic vacua. Finally, we show how to compute the number of chiral matter multiplets for this class of vacua allowing to discuss associated Yukawa couplings.

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Andreas

1999

Fortschr. Phys.

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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.

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Three-branes and five-branes in N=1 dual string pairs

Cited by 27 publications

References 8 publications

New aspects of Heterotic–F-theory duality

New aspects of Heterotic–F-theory duality

Comments on <i>N</i> = 1 Heterotic String Vacua

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