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 × (T2/ℤ2) 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.
Bergshoeff, E., Kallosh, R., Kashani Poor, A., Sorokin, D., Tomasiello, A. (2005). An Index for the Dirac operator on D3 branes with background fluxes. JOURNAL OF HIGH ENERGY PHYSICS(10), 102 [10.1088/1126-6708/2005/10/102].
An Index for the Dirac operator on D3 branes with background fluxes
TOMASIELLO, ALESSANDRO
2005
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 × (T2/ℤ2) 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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