Five-dimensional gauge theories are in general not well-defined as quantum field theories. The Yang-Mills coupling has dimension of mass^(-1/2), making these theories non-renormalizable, which means that we cannot consistently remove the UV cutoff used to regularize loop amplitudes. Physically the theories become strongly coupled in the UV, where they must be replaced by some “UV complete” theory. In some cases, however, Seiberg argued that there exist supersymmetric UV fixed points described by strongly interacting five-dimensional superconformal field theories, although these CFT’s do not seem to admit a Lagrangian description.
In view of the AdS/CFT duality it is natural to wonder whether these 5d CFT’s admit 6d AdS gravity duals. This case of the AdS/CFT correspondence has been the least studied. It is complicated by the fact that the amount of supersymmetry is reduced relative to the maximal supersymmetry cases in other dimensions, making it harder to find 6d AdS solutions by dimensional reduction of supergravity. The first explicit example was found by Brandhuber and Oz, who made use of a brane construction in string theory to relate the fixed point CFT of a particular 5d gauge theory based on the gauge group USp(2N) to a ten-dimensional geometry with a non-compact 6d AdS component and a compact 4-sphere.
Recently, O. Bergman and D. Rodriguez-Gomez have generalized this case to three classes of 5d supersymmetric gauge theories involving products of symplectic and unitary groups, and argued that they are dual to geometries where the compact part is replaced by an orbifold of a 4-sphere. These new examples allow for several non-trivial checks of the duality, by comparing various wrapping modes of branes on compact cycles with operators in the 5d CFT that carry the corresponding global symmetry charges. This also opens the door to a number of further generalizations related to the possibility of turning on various fluxes on the cycles.