TY - JOUR

T1 - Flux compactifications on projective spaces and the S-duality puzzle

AU - Bouwknegt, Peter

AU - Evslin, Jarah

AU - Jurčo, Branislav

AU - Mathai, Varghese

AU - Sati, Hisham

PY - 2006/6

Y1 - 2006/6

N2 - 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}P3 × R{double-struck}P2k+1 × S6-2k with torsion H-flux and to demonstrate the conjectured T-duality to S3 × S2k+1 × S6-2k 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.

AB - 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}P3 × R{double-struck}P2k+1 × S6-2k with torsion H-flux and to demonstrate the conjectured T-duality to S3 × S2k+1 × S6-2k 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.

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U2 - 10.4310/ATMP.2006.v10.n3.a3

DO - 10.4310/ATMP.2006.v10.n3.a3

M3 - Article

AN - SCOPUS:33846133659

VL - 10

SP - 345

EP - 394

JO - Advances in Theoretical and Mathematical Physics

JF - Advances in Theoretical and Mathematical Physics

SN - 1095-0761

IS - 3

ER -