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Kaehler metrics and gauge kinetic functions for intersecting D6-branes on toroidal orbifolds - The complete perturbative story

We systematically derive the perturbatively exact holomorphic gauge kinetic function, the open string Kaehler metrics and closed string Kaehler potential on intersecting D6-branes by matching open string one-loop computations of gauge thresholds with field theoretical gauge couplings in N=1 supergravity. We consider all cases of bulk, fractional and rigid D6-branes on T6/OR and the orbifolds T6/(Z(N)xOR) and T6/(Z(2)xZ(2M)xOR) without and with discrete torsion, which differ in the number of bulk complex structures and in the bulk Kaehler potential. Our analysis includes all supersymmetric configurations of vanishing and non-vanishing angles among D6-branes and O6-planes, and all possible Wilson line and displacement moduli are taken into account. The shape of the Kaehler moduli turns out to be orbifold independent but angle dependent, whereas the holomorphic gauge kinetic functions obtain three different kinds of one-loop corrections: a Kaehler moduli dependent one for some vanishing angle independently of the orbifold background, another one depending on complex structure moduli only for fractional and rigid D6-branes, and finally a constant term from intersections with O6-planes. These results are of essential importance for the construction of the related effective field theory of phenomenologically appealing D-brane models. As first examples, we compute the complete perturbative gauge kinetic functions and Kaehler metrics for some T6/Z(2)xZ(2) models with rigid D-branes of arXiv:0902.1694 [hep-th] by Angelantonj et al. As a second class of examples, the Kaehler metrics and gauge kinetic functions for the fractional QCD and leptonic D6-brane stacks of the Standard Model on T6/Z(6') from arXiv:0806.3039 [hep-th] by Gmeiner and Honecker are given.