Bjorn Andreas

From local to global in F-theory model building

Abstract When locally engineering F-theory models some D 7 -branes for the gauge group factors are specified and matter is localized on the intersection curves of the compact parts of the world-volumes. In this note, we discuss to what extent one can draw conclusions about F-theory models by just restricting the attention locally to a particular seven-brane. Globally, the possible D 7 -branes are not independent from each other and the (compact part of the) D 7 -brane can have unavoidable intrinsic singularities. Many special intersecting loci which were not chosen by hand occur inevitably, notably codimension-three loci which are not intersections of matter curves. We describe these complications specifically in a global S U ( 5 ) model and also their impact on the tadpole cancellation condition.

On vector bundles and chiral matter in N = 1 heterotic compactifications

In this note we derive the net number of generations of chiral fermions in heterotic string compactifications on Calabi-Yau threefolds with SU(n) vector bundles, for n odd, using the parabolic approach for bundles. This extends the work of Friedman, Morgan and Witten, who treated SU(n) vector bundles, with n even, which lead to a vanishing net amount of chiral matter. We then compare our results with the spectral cover construction for bundles and make a comment on the net number interpretation in F-theory.

Solutions of the Strominger System via Stable Bundles on Calabi-Yau Threefolds

We prove that a given Calabi-Yau threefold with a stable holomorphic vector bundle can be perturbed to a solution of the Strominger system provided that the second Chern class of the vector bundle is equal to the second Chern class of the tangent bundle. If the Calabi-Yau threefold has strict SU(3) holonomy then the equations of motion derived from the heterotic string effective action are also satisfied by the solutions we obtain.

THREE-BRANES AND FIVE-BRANES IN N = 1 DUAL STRING PAIRS

Abstract In this note we show that in dual N =1 string vacua provided by the heterotic string on an elliptic Calabi-Yau together with a vector bundle respectively F -theory on Calabi-Yau fourfold the number of heterotic fivebranes necessary for anomaly cancellation matches the number of F -theory threebranes necessary for tadpole cancellation. This extends to the general case the work of Friedman, Morgan and Witten, who treated the case of embedding a heterotic E 8 × E 8 bundle, leaving no unbroken gauge group, where one has a smooth Weierstrass model on the F -theory side.

N = 1 dual string pairs and their massless spectra

Abstract We construct two chains of four-dimensional F-theory/heterotic dual string pairs with N = 1 supersymmetry. On the F-theory side as well as on the heterotic side the geometry of the involved manifolds relies on del Pezzo surfaces. We match the massless spectra by using, for one chain of models, an index formula to count the heterotic bundle moduli and determine the dual F-theory spectra from the Hodge numbers of the four-folds X 4 and of the type 1113 base spaces.

Heterotic Non-Kahler Geometries via Polystable Bundles on Calabi-Yau Threefolds

Abstract In arXiv:1008.1018 it is shown that a given stable vector bundle V on a Calabi–Yau threefold X which satisfies c 2 ( X ) = c 2 ( V ) can be deformed to a solution of the Strominger system and the equations of motion of heterotic string theory. In this note we extend this result to the polystable case and construct explicit examples of polystable bundles on elliptically fibered Calabi–Yau threefolds where it applies. The polystable bundle is given by a spectral cover bundle, for the visible sector, and a suitably chosen bundle, for the hidden sector. This provides a new class of heterotic flux compactifications via non-Kahler deformation of Calabi–Yau geometries with polystable bundles. As an application, we obtain examples of non-Kahler deformations of some three generation GUT models.

Spectral bundles and the DRY-Conjecture

Abstract Supersymmetric heterotic string models, built from a Calabi–Yau threefold X endowed with a stable vector bundle V , usually start from a phenomenologically motivated choice of a bundle V v in the visible sector, the spectral cover construction on an elliptically fibered X being a prominent example. The ensuing anomaly mismatch between c 2 ( V v ) and c 2 ( X ) , or rather the corresponding differential forms, is often ‘solved’, on the cohomological level, by including a fivebrane. This leads to the question whether the difference can be alternatively realized by a further stable bundle. The ‘DRY’-conjecture of Douglas, Reinbacher and Yau in math.AG/0604597 gives a sufficient condition on cohomology classes on X to be realized as the Chern classes of a stable sheaf. In 1010.1644 [hep-th], we showed that infinitely many classes on X exist for which the conjecture is true. In this note, we give the sufficient condition for the mentioned fivebrane classes to be realized by a further stable bundle in the hidden sector. Using a result obtained in 1011.6246 [hep-th], we show that corresponding bundles exist, thereby confirming this version of the DRY-Conjecture.

On possible Chern classes of stable bundles on Calabi–Yau threefolds

Abstract Supersymmetric heterotic string models, built from a Calabi–Yau threefold X endowed with a stable vector bundle V , usually lead to an anomaly mismatch between c 2 ( V ) and c 2 ( X ) ; this leads to the question whether the difference can be realized by a further bundle in the hidden sector. In [M.R. Douglas, R. Reinbacher, S.-T. Yau, Branes, Bundles and Attractors: Bogomolov and Beyond, math.AG/0604597], a conjecture is stated which gives sufficient conditions on cohomology classes on X to be realized as the Chern classes of a stable reflexive sheaf V ; a weak version of this conjecture predicts the existence of such a V if c 2 ( V ) is of a certain form. In this note, we prove that on elliptically fibered X infinitely many cohomology classes c ∈ H 4 ( X , Z ) exist which are of this form and for each of them a stable S U ( n ) vector bundle with c = c 2 ( V ) exists.

STABLE SHEAVES OVER K3 FIBRATIONS

We construct stable sheaves over K3 fibrations using a relative Fourier-Mukai transform which describes the sheaves in terms of spectral data similar to the construction for elliptic fibrations. On K3 fibered Calabi-Yau threefolds we show that the Fourier-Mukai transform induces an embedding ion of the relative Jacobian of spectral line bundles on spectral covers into the moduli space of sheaves of given invariants. This makes the moduli space of spectral sheaves to a generic torus fibration over the moduli space of curves of given arithmetic genus on the Calabi-Yau manifold.

A note on a class of cosmological string backgrounds

We study a class of four dimensional, anisotropic string backgrounds and analyse their expansion and singularity structure. We will see how O(3,3) duality acts on this class and in particular realizes the Brandenberger-Vafa scenario.