Rigid Holography and Six-Dimensional N=(2,0) Theories on AdS₅ times S¹

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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 (CFTs), this relates some of the observables of these field theories on AdS to a subsector of the dual CFTs. We exemplify this `rigid holography' by studying in detail the 6d N=(2,0) Aₖ₋₁ superconformal field theory (SCFT) on AdS₅xS¹, with equal radii for AdS₅ and for S¹. We choose specific boundary conditions preserving sixteen supercharges that arise when this theory is embedded into Type IIB string theory on AdS₅xS⁵/Zₖ. On R⁴,¹xS¹, this 6d theory has a 5(K-1)-dimensional moduli space, with unbroken 5d SU(K) gauge symmetry at (and only at) the origin. On AdS₅xS¹, 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 5d gauge theory is coupled to a 4d 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 4d 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 6d N=(2,0) theory on AdS₅xS¹ with sources on the boundary is a subsector of the large N limit of various 4d N=2 quiver SCFTs that remains non-trivial in the large N limit. The same subsector appears universally in many different 4d N=2 SCFTs. We also discuss a decoupling limit that leads to N=(2,0) `little string theories' on AdS₅xS¹.