Triality in Little String Theories

We study a class of eight-supercharge little string theories (LSTs) on the world volume of N M5-branes with transverse space S-1 x (C(2/)Z(M)). These M-brane configurations compactified on a circle are dual to M D5-branes intersecting N NS5-branes on T-2 x R-7,R-1 as well as to F-theory compactified on a toric Calabi-Yau threefold X-N,X- M. We argue that the Kahler cone of X-N,X- M admits three regions associated with weakly coupled quiver gauge theories of gauge groups [U(N)](M), [U(M)](N), and [U(NM/k)](k) where k = gcd(N, M). These provide low-energy descriptions of different LSTs. The duality between the first two gauge theories is well known and is a consequence of the S-duality between D5- and NS5-branes or the T-duality of the LSTs. The triality involving the third gauge theory is new, and we demonstrate it using several examples. We also discuss implications of this triality for the W-algebras associated with the Alday-Gaiotto-Tachikawa dual theories.