Open Access
June 2006 Flux compactifications on projective spaces and the $S$-duality puzzle
Jarah Evslin, Peter Bouwknegt, Branislav Jurčo, Varghese Mathai, Hisham Sati
Adv. Theor. Math. Phys. 10(3): 345-394 (June 2006).


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 $\mathbb{R}P^3\times\mathbb{R}P^{2k+1}\times S^{6-2k}$ with torsion $H$-flux and to demonstrate the conjectured $T$-duality to $S^3\times S^{2k+1}\times S^{6-2k}$ with no flux. When $k=1$, $H\neq 0$ 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.


Download Citation

Jarah Evslin. Peter Bouwknegt. Branislav Jurčo. Varghese Mathai. Hisham Sati. "Flux compactifications on projective spaces and the $S$-duality puzzle." Adv. Theor. Math. Phys. 10 (3) 345 - 394, June 2006.


Published: June 2006
First available in Project Euclid: 30 July 2006

zbMATH: 1129.81062
MathSciNet: MR2250274

Rights: Copyright © 2006 International Press of Boston

Vol.10 • No. 3 • June 2006
Back to Top