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Abstract: As a step towards the classification of supergravity backgrounds with flux,we study the back-reacted geometry created by a BPS M2-brane when it wraps acycle in a Calabi-Yau manifold. If it is to preserve supersymmetry, themembrane background must obey certain conditions. These conditions areexpressed as geometrical constraints on differential forms and as such, can beinterpreted as calibrations. Knowing the complete set of calibrations is thesame as satisfying all conditions needed for supersymmetry preservation. Whilea purely geometric background is completely specified through standardcalibrations, in order to fully describe a flux background, we must also stateits generalized calibrations. These can be found by probing the background withBPS branes. The logic is simple. Since a BPS probe is guaranteed to be stable,we require that its volume be given by a calibrated form. This applies equallyto both charged and uncharged probes; the former are stabilized by flux whereasthe latter achieve stability by minimizing their volumes. Volume-forms ofcharged probes correspond to generalized calibrations and those of unchargedprobes, to standard calibrations. Previously geometries were probed only byuncharged branes. The calibrations that were found had then to be supplementedby additional conditions in order to guarantee supersymmetry preservation inbackgrounds with flux. Once the scope is broadened to include charged branes,the -missing conditions- generalized calibrations can also be recovered usingthe probe analysis. We use this method to classify the backgrounds of wrappedM2-branes embedded in Calabi-Yau manifolds by specifying their calibrations.



Author: Tasneem Zehra Husain

Source: https://arxiv.org/



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