We study a class of eight-supercharge little string theories (LSTs) on the world volume of $N$ M5-branes with transverse space ${\mathbb{S}}^1\times ({\mathbb{C}}^2/{\mathbb{Z}}_M)$. These M-brane configurations compactified on a circle are dual to $M$ D5-branes intersecting $N$ NS5-branes on ${\mathbb{T}}^2\times {\mathbb{R}}^{7,1}$ as well as to F-theory compactified on a toric Calabi-Yau threefold $X_{N,M}$. We argue that the Kähler cone of $X_{N,M}$ admits three regions associated with weakly coupled quiver gauge theories of gauge groups $[U(N){]}^M,[U(M){]}^N$, and $[U(\frac{NM}{k}){]}^k$ 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.

• Received 6 December 2017

DOI:https://doi.org/10.1103/PhysRevD.97.046004

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Published by the American Physical Society