# Holographic duals of (super)gravity sigma models

Consider a (super)gravity theory on asymptotically AdS spacetime $$N$$ with fixed conformal boundary $$\partial N$$ coupled to scalars $$\phi_i$$ taking values in a manifold $$M$$, possibly in addition to other kinds of fields. Assuming the AdS/CFT conjecture, this is dual to some (supersymmetric) field theory on $$\partial N$$. I expect the field content of this theory to be sections of the pullback of a certain bundle or fibration over $$M$$ along the map $$\phi_0:\partial N\rightarrow M$$ defined by the boundary values of the scalars $$\phi^i$$. Is anything known about what bundle or fibration this is?