### Abstract

We study D-branes and Ramond-Ramond fields on global orbifolds of Type II string theory with vanishing H-flux using methods of equivariant K-theory and K-homology. We illustrate how Bredon equivariant cohomology naturally realizes stringy orbifold cohomology. We emphasize its role as the correct cohomological tool which captures known features of the low-energy effective field theory, and which provides new consistency conditions for fractional D-branes and Ramond-Ramond fields on orbifolds. We use an equivariant Chern character from equivariant K-theory to Bredon cohomology to define new Ramond-Ramond couplings of D-branes which generalize previous examples. We propose a definition for groups of differential characters associated to equivariant K-theory. We derive a Dirac quantization rule for Ramond-Ramond fluxes, and study flat Ramond-Ramond potentials on orbifolds. © Springer-Verlag 2009.

Original language | English |
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Pages (from-to) | 647-702 |

Number of pages | 56 |

Journal | Communications in Mathematical Physics |

Volume | 294 |

Issue number | 3 |

DOIs | |

Publication status | Published - Jan 2010 |

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## Cite this

*Communications in Mathematical Physics*,

*294*(3), 647-702. https://doi.org/10.1007/s00220-009-0975-1