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Field theories on anti-de Sitter (AdS) space can be studied by realizing themas 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 vacuaare dual to conformal field theories (CFTs), this relates some of theobservables of these field theories on AdS to a subsector of the dual CFTs. Weexemplify this `rigid holography' by studying in detail the 6d N=(2,0) A_{K-1}superconformal field theory (SCFT) on AdS_5xS^1, with equal radii for AdS_5 andfor S^1. We choose specific boundary conditions preserving sixteen superchargesthat arise when this theory is embedded into Type IIB string theory onAdS_5xS^5/Z_K. On R^{4,1}xS^1, this 6d theory has a 5(K-1)-dimensional modulispace, with unbroken 5d SU(K) gauge symmetry at (and only at) the origin. OnAdS_5xS^1, the theory has a 2(K-1)-dimensional `moduli space' of supersymmetricconfigurations. We argue that in this case the SU(K) gauge symmetry is unbrokeneverywhere in the `moduli space' and that this 5d gauge theory is coupled to a4d theory on the boundary of AdS_5 whose coupling constants depend on the`moduli'. This involves non-standard boundary conditions for the gauge fieldson AdS_5. Near the origin of the `moduli space', the theory on the boundarycontains a weakly coupled 4d N=2 supersymmetric SU(K) gauge theory. We showthat this implies large corrections to the metric on the `moduli space'. Theembedding in string theory implies that the 6d N=(2,0) theory on AdS_5xS^1 withsources on the boundary is a subsector of the large N limit of various 4d N=2quiver SCFTs that remains non-trivial in the large N limit. The same subsectorappears universally in many different 4d N=2 SCFTs. We also discuss adecoupling limit that leads to N=(2,0) `little string theories' on AdS_5xS^1.

Rigid Holography and Six-Dimensional N=(2,0) Theories on AdS_5 times S^1