## Abstract

We derive a formula for D3-brane charge on a compact spacetime, which includes torsion corrections to the tadpole cancellation condition. We use this to classify D-branes and Ramond-Ramond fluxes in type II string theory on R{double-struck}P^{3} × R{double-struck}P^{2k+1} × S^{6-2k} with torsion H-flux and to demonstrate the conjectured T-duality to S^{3} × S^{2k+1} × S^{6-2k} with no flux. When k = 1, H = 0 and so the K-theory that classifies fluxes is twisted. When k = 2, the square of the H-flux yields an S-dual Freed- Witten anomaly, which is canceled by a D3-brane insertion that ruins the dual K-theory flux classification. When k = 3, the cube of H is nontrivial and so the D3 insertion may itself be inconsistent and the compactification unphysical. Along the way we provide a physical interpretation for the Atiyah-Hirzebruch spectral sequence in terms of the boundaries of branes within branes.

Original language | English (US) |
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Pages (from-to) | 345-394 |

Number of pages | 50 |

Journal | Advances in Theoretical and Mathematical Physics |

Volume | 10 |

Issue number | 3 |

DOIs | |

State | Published - Jun 2006 |

## ASJC Scopus subject areas

- Mathematics(all)
- Physics and Astronomy(all)