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K-theory (physics) : ウィキペディア英語版 | K-theory (physics)
In string theory, the K-theory classification refers to a conjectured application of K-theory (in abstract algebra and algebraic topology) to superstrings, to classify the allowed Ramond–Ramond field strengths as well as the charges of stable D-branes. In condensed matter physics K-theory has also found important applications, specially in the topological classification of topological insulators, superconductors and stable Fermi surfaces (, ). == History ==
This conjecture, applied to D-brane charges, was first proposed by . It was popularized by who demonstrated that in type IIB string theory arises naturally from Ashoke Sen's realization of arbitrary D-brane configurations as stacks of D9 and anti-D9-branes after tachyon condensation. Such stacks of branes are inconsistent in a non-torsion Neveu–Schwarz (NS) 3-form background, which, as was highlighted by , complicates the extension of the K-theory classification to such cases. suggested a solution to this problem: D-branes are in general classified by a twisted K-theory, that had earlier been defined by .
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