Rigid Holography and Six-Dimensional N=(2,0) Theories on AdS_5 times S^1 (original) (raw)
2015, arXiv (Cornell University)
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 antide Sitter space to a subsector of the dual conformal field theories. We exemplify this 'rigid holography' by studying in detail the six-dimensional N = (2, 0) A K−1 superconformal field theory (SCFT) on AdS 5 × S 1 , with equal radii for AdS 5 and for S 1. We choose specific boundary conditions preserving sixteen supercharges that arise when this theory is embedded into Type IIB string theory on AdS 5 ×S 5 /Z K. On R 4,1 ×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 AdS 5 × 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 fivedimensional gauge theory is coupled to a four-dimensional theory on the boundary of AdS 5 whose coupling constants depend on the 'moduli'. This involves non-standard boundary conditions for the gauge fields on AdS 5. Near the origin of the 'moduli space', the theory on the boundary contains a weakly coupled four-dimensional 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 N = (2, 0) theory on AdS 5 × S 1 with sources on the boundary is a subsector of the large N limit of various four-dimensional N = 2 quiver SCFTs that remains non-trivial in the large N limit. The same subsector appears universally in many different four-dimensional N = 2 SCFTs. We also discuss a decoupling limit that leads to N = (2, 0) 'little string theories' on AdS 5 × S 1 .
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