Triality in Little String Theories

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

49 pages

References in corpus (11)

• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• The Refined Topological Vertex
• 6d Conformal Matter
• Toda Theories, Matrix Models, Topological Strings, and N=2 Gauge Systems
• Anomaly polynomial of general 6d SCFTs
• E + E $\to$ H
• ADE Little String Theory on a Riemann Surface (and Triality)
• M-theory on Elliptic Calabi-Yau Threefolds and 6d Anomalies
• Bound States of Little Strings and Symmetric Orbifold CFTs
• Five-Brane Webs and Highest Weight Representations
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Cited by in corpus (20)

• 2-Group Symmetries of 6d Little String Theories and T-duality
• Universal Features of BPS Strings in Six-dimensional SCFTs
• Revisiting the classifications of 6d SCFTs and LSTs
• A slow review of the AGT correspondence
• Back to Heterotic Strings on ALE Spaces: Part I -- Instantons, 2-groups and T-duality
• From Little String Free Energies Towards Modular Graph Functions
• Beyond Triality: Dual Quiver Gauge Theories and Little String Theories
• 3d Mirror Symmetry from S-duality
• Five-Dimensional Gauge Theories from Shifted Web Diagrams
• Intersecting Defects and Supergroup Gauge Theory
• Dihedral Symmetries of Gauge Theories from Dual Calabi-Yau Threefolds
• Elliptic lift of the Shiraishi function as a non-stationary double-elliptic function
• The ABCDEFG of Little Strings
• Four flavours, triality and bimodular forms
• Quiver ${\text{W}}_{{\epsilon }_1,{\epsilon }_2}$ algebras of 4d $\mathcal{N}=2$ gauge theories
• Diagrammatic Expansion of Non-Perturbative Little String Free Energies
• Symmetric Orbifold Theories from Little String Residues
• Symmetries in A-Type Little String Theories, Part I
• A Representation-Theoretic Approach to $qq$-Characters
• Non-perturbative Symmetries of Little Strings and Affine Quiver Algebras