![]() In the classical limit of type II string theory, which is type II supergravity, the Ramond–Ramond field strengths are differential forms. Alternately one may use the K-theory of a 9-dimensional time slice as has been done by Maldacena, Moore & Seiberg (2001). One needs to choose a half of the fluxes to quantize, or a polarization in the geometric quantization-inspired language of Diaconescu, Moore, and Witten and later of Varghese & Sati (2004). However Chern characters are always rational, and so the K-theory classification must be replaced. Thus not all of the RR fluxes, which are interpreted as the Chern characters in K-theory, can be rational. The duality uses the Hodge star, which depends on the metric and so is continuously valued and in particular is generically irrational. ![]() In addition, if one attempts to classify fluxes on a compact ten-dimensional spacetime, then a complication arises due to the self-duality of the RR fluxes. Diaconescu, Moore & Witten (2003) argued that the K-theory classification is incompatible with S-duality in IIB string theory. Recently K-theory has been conjectured to classify the spinors in compactifications on generalized complex manifolds.ĭespite these successes, RR fluxes are not quite classified by K-theory. ![]() K-theory has also been used to conjecture a formula for the topologies of T-dual manifolds by Bouwknegt, Evslin & Varghese (2004). Uranga (2001) applied the K-theory classification to derive new consistency conditions for flux compactifications. For example, Hanany & Kol (2000) used it to argue that there are eight species of orientifold one-plane. The K-theory classification of D-branes has had numerous applications. Bouwknegt & Varghese (2000) suggested a solution to this problem: D-branes are in general classified by a twisted K-theory, that had earlier been defined by Rosenberg (1989). Such stacks of branes are inconsistent in a non-torsion Neveu–Schwarz (NS) 3-form background, which, as was highlighted by Kapustin (2000), complicates the extension of the K-theory classification to such cases. It was popularized by Witten (1998) 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. This conjecture, applied to D-brane charges, was first proposed by Minasian & Moore (1997). 10 References (condensed matter physics).5 Reconciling twisted K-theory and S-duality.4.3 Twisted K-theory from MMS instantons.
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