Field theories on anti-de Sitter (AdS) space can be studied by realizing them as low-energy limits of AdS vacua of string/M theory. In an appropriate limit, the field theories decouple from the rest of string/M theory. Since these vacua are dual to conformal field theories, this relates some of the observables of these field theories on AdS space to a subsector of the dual conformal field theories. We exemplify this ‘rigid holography’ by studying in detail the six-dimensional $$ \mathcal{N}=\left(2,0\right) $$ A K − 1 superconformal field theory (SCFT) on AdS5 × $$ \mathbb{S} $$ 1, with equal radii for AdS5 and for $$ \mathbb{S} $$ 1. We choose specific boundary conditions preserving sixteen supercharges that arise when this theory is embedded into Type IIB string theory on AdS5 × $$ \mathbb{S} $$ 5/ℤ K . On ℝ4,1 × $$ \mathbb{S} $$ 1, this six-dimensional theory has a 5(K − 1)-dimensional moduli space, with unbroken five-dimensional SU(K) gauge symmetry at (and only at) the origin. On AdS5 × $$ \mathbb{S} $$ 1, the theory has a 2(K − 1)-dimensional ‘moduli space’ of supersymmetric configurations. We argue that in this case the SU(K) gauge symmetry is unbroken everywhere in the ‘moduli space’ and that this five-dimensional gauge theory is coupled to a four-dimensional theory on the boundary of AdS5 whose coupling constants depend on the ‘moduli’. This involves non-standard boundary conditions for the gauge fields on AdS5. Near the origin of the ‘moduli space’, the theory on the boundary contains a weakly coupled four-dimensional $$ \mathcal{N}=2 $$ supersymmetric SU(K) gauge theory. We show that this implies large corrections to the metric on the ‘moduli space’. The embedding in string theory implies that the six-dimensional $$ \mathcal{N}=\left(2,0\right) $$ theory on AdS5 × $$ \mathbb{S} $$ 1 with sources on the boundary is a subsector of the large N limit of various four-dimensional $$ \mathcal{N}=2 $$ quiver SCFTs that remains non-trivial in the large N limit. The same subsector appears universally in many different four-dimensional $$ \mathcal{N}=2 $$ SCFTs. We also discuss a decoupling limit that leads to $$ \mathcal{N}=\left(2,0\right) $$ ‘little string theories’ on AdS5 × $$ \mathbb{S} $$ 1.