 The above equation is not invariant under S-duality, which exchanges G3 and H. Instead Diaconescu, Moore, and Witten have proposed the following S-duality covariant extension

where P is an unknown characteristic class that depends only on the topology, and in particular not on the fluxes.have found a constraint on P using the E8 gauge theory approach to M-theory pioneered by Diaconescu, Moore, and Witten.Thus D-branes in IIB are not classified by twisted K-theory after all, but some unknown S-duality-covariant object that inevitably also classifies both fundamental strings and NS5-branes.