What Does(n't) K-theory Classify?

Details What Does(n't) K-theory Classify? What Does(n't) K-theory Classify?

2006-10-31

arxiv.org/abs/hep-th/0610328v1

Physics

High Energy Physics

High Energy Physics - Theory

91 pages, 1 figure, Prepared for the Second Modave Summer School in Mathematical Physics

Scientific paper

We review various K-theory classification conjectures in string theory. Sen conjecture based proposals classify D-brane trajectories in backgrounds with no H flux, while Freed-Witten anomaly based proposals classify conserved RR charges and magnetic RR fluxes in topologically time-independent backgrounds. In exactly solvable CFTs a classification of well-defined boundary states implies that there are branes representing every twisted K-theory class. Some of these proposals fail to respect the self-duality of the RR fields in the democratic formulation of type II supergravity and none respect S-duality in type IIB string theory. We discuss two applications. The twisted K-theory classification has led to a conjecture for the topology of the T-dual of any configuration. In the Klebanov-Strassler geometry twisted K-theory classifies universality classes of baryonic vacua.

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