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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?

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