K-theory (physics)
In string theory, 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 . Applications The K-theory classification of D-branes has had numerous applications. For example, used it to argue that there are eight species of orientifold one-plane. applied the K-theory classification to derive new consistency conditions for flux compactifications. K-theory has also been used to conjecture a formula for