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

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 RP 3 × RP 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 FreedWitten 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.

Flux quantization and the M-theoretic characters

“…Any formalism which describes the structures in one theory should be compatible with that describing those in the dual theory. The compatibility of the K-theoretic description of the fields of type II supersting theories in ten dimensions with T-duality was studied in [14] and with S-duality in [15] [16].…”

A higher twist in string theory

“…This is zero if F 3 = 0, and so we have a complex if we restrict to the NS fields. In this case, one also has to deal with S-duality appropriately (see [9] and [23]) and this may require the use of the combined equation of motion…”

$T$-duality for torus bundles with $H$-fluxes via noncommutative topology. {II}. The high-dimensional case and the $T$-duality group

“…The element 1 2 0 0 −1 2 ∈ GO(2, 2; Z) replaces the original T-dual by the pair consisting of (S 7 × S 3 , 0), where S 3 and S 7 are given the inverse of the standard circle action, i.e., we change the signs of the Chern classes of the dual bundle. An alternate derivation of the T-dual based on physical arguments was given in [5].…”