21 research outputs found
Homological Type of Geometric Transitions
The present paper gives an account and quantifies the change in topology
induced by small and type II geometric transitions, by introducing the notion
of the \emph{homological type} of a geometric transition. The obtained results
agree with, and go further than, most results and estimates, given to date by
several authors, both in mathematical and physical literature.Comment: 36 pages. Minor changes: A reference and a related comment in Remark
3.2 were added. This is the final version accepted for publication in the
journal Geometriae Dedicat
Constraining the Kahler Moduli in the Heterotic Standard Model
Phenomenological implications of the volume of the Calabi-Yau threefolds on
the hidden and observable M-theory boundaries, together with slope stability of
their corresponding vector bundles, constrain the set of Kaehler moduli which
give rise to realistic compactifications of the strongly coupled heterotic
string. When vector bundles are constructed using extensions, we provide simple
rules to determine lower and upper bounds to the region of the Kaehler moduli
space where such compactifications can exist. We show how small these regions
can be, working out in full detail the case of the recently proposed Heterotic
Standard Model. More explicitely, we exhibit Kaehler classes in these regions
for which the visible vector bundle is stable. On the other hand, there is no
polarization for which the hidden bundle is stable.Comment: 28 pages, harvmac. Exposition improved, references and one figure
added, minor correction
Topological String Amplitudes, Complete Intersection Calabi-Yau Spaces and Threshold Corrections
We present the most complete list of mirror pairs of Calabi-Yau complete
intersections in toric ambient varieties and develop the methods to solve the
topological string and to calculate higher genus amplitudes on these compact
Calabi-Yau spaces. These symplectic invariants are used to remove redundancies
in examples. The construction of the B-model propagators leads to compatibility
conditions, which constrain multi-parameter mirror maps. For K3 fibered
Calabi-Yau spaces without reducible fibers we find closed formulas for all
genus contributions in the fiber direction from the geometry of the fibration.
If the heterotic dual to this geometry is known, the higher genus invariants
can be identified with the degeneracies of BPS states contributing to
gravitational threshold corrections and all genus checks on string duality in
the perturbative regime are accomplished. We find, however, that the BPS
degeneracies do not uniquely fix the non-perturbative completion of the
heterotic string. For these geometries we can write the topological partition
function in terms of the Donaldson-Thomas invariants and we perform a
non-trivial check of S-duality in topological strings. We further investigate
transitions via collapsing D5 del Pezzo surfaces and the occurrence of free Z2
quotients that lead to a new class of heterotic duals.Comment: 117 pages, 1 Postscript figur
Extremal Bundles on Calabi-Yau Threefolds
We study constructions of stable holomorphic vector bundles on CalabiâYau threefolds, especially those with exact anomaly cancellation which we call extremal. By going through the known databases we find that such examples are rare in general and can be ruled out for the spectral cover construction for all elliptic threefolds. We then introduce a general HartshorneâSerre construction and use it to find extremal bundles of general ranks and study their stability, as well as computing their Chern numbers. Based on both existing and our new constructions, we revisit the DRY conjecture for the existence of stable sheaves on Calabiâthreefolds, and provide theoretical and numerical evidence for its correctness. Our construction can be easily generalized to bundles with no extremal conditions imposed