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An index for the Dirac operator on D3 branes with background fluxes

Eric Bergshoeff·Renata Kallosh·Amir-Kian Kashani-Poor·Dmitri Sorokin·Alessandro Tomasiello
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Abstract

We study the problem of instanton generated superpotentials in Calabi-Yau orientifold compactifications directly in type IIB string theory. To this end, we derive the Dirac equation on a Euclidean D3 brane in the presence of background fluxes. We propose an index which governs whether the generation of a superpotential in the effective 4d theory by D3 brane instantons is possible. Applying the formalism to various classes of examples, including the K3 x T^2/Z_2 orientifold, in the absence and presence of fluxes, we show that our results are consistent with conclusions attainable via duality from an M-theory analysis.

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Eric Bergshoeff, Renata Kallosh, Amir-Kian Kashani-Poor, Dmitri Sorokin, Alessandro Tomasiello. 2006-04-22. An index for the Dirac operator on D3 branes with background fluxes. https://doi.org/10.1088/1126-6708%2F2005%2F10%2F102

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