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Can D-Branes Wrap Nonrepresentable Cycles?

Jarah Evslin·Hisham Sati
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Abstract

Sometimes a homology cycle of a nonsingular compactification manifold cannot be represented by a nonsingular submanifold. We want to know whether such nonrepresentable cycles can be wrapped by D-branes. A brane wrapping a representable cycle carries a K-theory charge if and only if its Freed-Witten anomaly vanishes. However some K-theory charges are only carried by branes that wrap nonrepresentable cycles. We provide two examples of Freed-Witten anomaly-free D6-branes wrapping nonrepresentable cycles in the presence of a trivial NS 3-form flux. The first occurs in type IIA string theory compactified on the Sp(2) group manifold and the second in IIA on a product of lens spaces. We find that the first D6-brane carries a K-theory charge while the second does not.

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Jarah Evslin, Hisham Sati. 2006-07-06. Can D-Branes Wrap Nonrepresentable Cycles?. https://doi.org/10.1088/1126-6708%2F2006%2F10%2F050

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