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

Abstract

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.

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

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Cited by in corpus (17)

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• Four-modulus "Swiss Cheese" chiral models
• D-brane networks in flux vacua, generalized cycles and calibrations
• Effects of brane-flux transition on black holes in string theory
• New N=1 dualities from orientifold transitions - Part II: String Theory
• M/F-Theory as Mf-Theory
• The character map in (twisted differential) non-abelian cohomology
• Ramond-Ramond fields and twisted differential K-theory
• Spherical T-Duality
• Freed-Witten anomaly in general flux compactification
• Finite Heisenberg Groups from Nonabelian Orbifold Quiver Gauge Theories
• Topics on the geometry of D-brane charges and Ramond-Ramond fields
• Topological strings live on attractive manifolds
• Half-flat Quantum Hair
• Comparing two approaches to the K-theory classification of D-branes
• Strongly coupled phases of $\mathcal{N}=1$ S-duality
• Twisted differential K-characters and D-branes