Authors: Gottfried Curio
Publish Date: 2010/08/19
Volume: 2010, Issue: 8, Pages: 92-
Abstract
For supersymmetric heterotic string compactifications on a CalabiYau threefold X endowed with a vector bundle V the worldsheet superpotential W is a sumof contributions from isolated rational curves mathcalC in X the individual contribution is given by an exponential in the Kähler class of the curve times a prefactor given essentially by the Pfaffian which depends on the moduli of V and the complex structure moduli of X Solutions of DW = 0 or even of DW = W = 0 can arise either by nontrivial cancellations between the individual terms in the summation over all contributing curves or because each of these terms is zero already individually Concerning the latter case conditions on the moduli making a single Pfaffian vanish for special moduli values have been investigated However even if corresponding moduli — fulfilling these constraints — for the individual contribution of one curve are known it is not at all clear whether one choice of moduli exists which fulfills the corresponding constraints for all contributing curves simultaneously Clearly this will in general happen only if the conditions on the ‘individual zeroes’ had already a conceptual origin which allows them to fit together consistently We show that this happens for a class of cases In the special case of spectral cover bundles we show that a relevant solution set has an interesting location in moduli space and is related to transitions which change the generation number
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