Triality in Little String Theories

TL;DR

This paper uncovers a novel triality among three different gauge theory descriptions of certain little string theories, revealing deep dualities linked to M-branes, D-branes, and F-theory compactifications.

Contribution

It introduces a new triality involving three gauge theories related to M5-branes and F-theory, expanding the understanding of dualities in little string theories.

Findings

Identification of three regions in the Kähler cone corresponding to different gauge theories.

Demonstration of the triality through explicit examples.

Discussion of implications for W-algebras and AGT dualities.

Abstract

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 K\"ahler 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 $k=\mbox{gcd}(N,M)$. 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.