I have a general or overview question related to charges on D- Branes lies in the K theory of Spacetime. We normally think charges of D branes lies in the Cohomology like $D_0$ branes couple to RR-1 form and so on.
The whole idea behind AdS/CFT duality (Maldacena' paper) is based on the fact that D-branes couple to RR form and it curves the spacetime. Can we think of this duality in terms of K-theory? By thinking in terms of K theory will give something new in this Holography business.
This is a good question which -- as far as I am aware -- has received little to no attention (but see below).
On the one hand it is clear why the question is outside the scope of traditional discussions:
AdS/CFT is commonly practiced in the large-$N$ limit of a huge (in fact humongous) number $N$ of branes. In this limit the branes are classical, in fact they are well-described by the eponymous asymptotic AdS-throats in (super-)gravity. But the stable branes that K-theory sees beyond this limit are quantum states, as witnessed by the fact that they are torsion subgroup elements in K-theory -- meaning that some finite multiple of them vanishes, so that a large $N$-limit does not even make sense for them.
On the other hand, the AdS/CFT correspondence may be and originally was conjectured to hold (see here) also for small $N$ (large $1/N$), in which case, however, it no longer involves (super-)gravity but full-blown strongly-coupled string theory aka "M-theory". It was fashionable at some point to hence claim that AdS/CFT defines M-theory in the small $N$-limit, but not much technical discussion of what this entails has ensued.
Of course this case of small $N$ -- in which, yes, D-branes will have to be described by K-theory -- is the case ultimately of interest in AdS/QCD: here $N = 3 \ll \infty$.
One place that comments on K-theory in non-perturbative holography is a note we are preparing, see Remark 2.8 at Anyonic topological order in TED K-theory.
