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Bjorn Andreas

Publications and source records attributed to Bjorn Andreas.

26 records · Page 2Linked to original sources
arXiv2004

U(n) Vector Bundles on Calabi-Yau Threefolds for String Theory Compactifications

An explicit description of the spectral data of stable U(n) vector bundles on elliptically fibered Calabi-Yau threefolds is given, extending previous work of Friedman, Morgan and Witten. The characteristic classes are computed and it is shown that part of the bundle cohomology vanishes. The stability and the dimension of the moduli space of the U(n) bundles are discussed. As an application, it is shown that the U(n) bundles are capable to solve the basic topological constraints imposed by heterotic string theory. Various explicit solutions of the Donaldson-Uhlenbeck-Yau equation are given. The heterotic anomaly cancellation condition is analyzed; as a result an integral change in the number of fiber wrapping five-branes is found. This gives a definite prediction for the number of three-branes in a dual F-theory model. The net-generation number is evaluated, showing more flexibility compared with the SU(n) case.

hep-th↗
arXiv2003

Comments on N=1 Heterotic String Vacua

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 an 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 the associated Yukawa couplings.

hep-th↗
arXiv2001

Fibrewise T-Duality for D-Branes on Elliptic Calabi-Yau

Fibrewise T-duality (Fourier-Mukai transform) for D-branes on an elliptic Calabi-Yau $X$ is shown to require naturally an appropriate twisting of the operation respectively a twisted charge. The fibrewise T-duality is furthermore expressed through known monodromies in the context of Kontsevich's interpretation of mirror symmetry.

hep-th↗
arXiv2000

Fourier-Mukai Transform and Mirror Symmetry for D-Branes on Elliptic Calabi-Yau

Fibrewise T-duality (Fourier-Mukai transform) for D-branes on an elliptic Calabi-Yau three-fold $X$ is seen to have an expected adiabatic form for its induced cohomology operation only when an appropriately twisted operation resp. twisted charge is defined. Some differences with the case of $K3$ as well as connections with the spectral cover construction for bundles on $X$ are pointed out. In the context of mirror symmetry Kontsevich's association of line bundle twists (resp. a certain 'diagonal' operation) with monodromies (esp. the conifold monodromy) is made explicit and checked for two example models. Interpreting this association as a relation between FM transforms and monodromies, we express the fibrewise FM transform through known monodromies. The operation of fibrewise duality as well as the notion of a certain index relevant to the computation of the moduli space of the bundle is transported to the sLag side. Finally the moduli space for D4-branes and its behaviour under the FM transform is considered with an application to the spectral cover.

math.AG↗
arXiv2000

Anomalous D-Brane Charge in F-Theory Compactifications

Tadpole cancellation in F-theory on an elliptic Calabi-Yau fourfold $X\to B_3$ demands some spacetime-filling three-branes (points in $B_3$). If moved to the discriminant surface, which supports the gauge group, and dissolved into a finite size instanton, the second Chern class of the corresponding bundle $E$ is expected to give a compensating contribution. However the dependence of D-brane charge on the geometry of $W$ and on the embedding $i: W\to B_3$ gives a correction to $c_2(E)$. We show how this is reconciled by considering the torsion sheaf $i_*E$ and discuss some integrality issues related to global properties of $X$ as well as the moduli space of this object.

hep-th↗
arXiv1999

Horizontal and Vertical Five-Branes in Heterotic/F-Theory Duality

We consider the heterotic string on an elliptic Calabi-Yau three-fold with five-branes wrapping curves in the base ('horizontal' curves) of the Calabi-Yau as well as some elliptic fibers ('vertical' curves). We show that in this generalized set-up, where the association of the heterotic side with the $F$-theory side is changed relative to the purely vertical situation, the number of five-branes wrapping the elliptic fibers still matches the corresponding number of $F$-theory three-branes.

hep-th↗
arXiv1998

N=1 Heterotic/F-Theory Duality

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.

hep-th↗