We initiate the study of (2,0) little string theory of ADE type using its definition in terms of IIB string compactified on an ADE singularity. As one application, we derive a 5d ADE quiver gauge theory that describes the little string compactified o
n a sphere with three full punctures, at low energies. As a second application, we show the partition function of this theory equals the 3-point conformal block of ADE Toda CFT, q-deformed. To establish this, we generalize the A_n triality of cite{AHS} to all ADE Lie algebras; IIB string perspective is crucial for this as well.
This is the 12th article in the collection of reviews Exact results on N=2 supersymmetric gauge theories ed. J. Teschner. This article describes one way to understand an important part of the AGT-correspondence in terms of a triality between four-dim
ensional gauge theory, the two-dimensional theory of its vortices, and conformal field theory. This triality is related to, and inspired by known large $N$ dualities of the topological string. It leads to a proof of some cases of the AGT-correspondence, and most importantly, of a generalisation of this correspondence to certain five-dimensional gauge theories.
