Beyond Triality: Dual Quiver Gauge Theories and Little String Theories

Abstract

The web of dual gauge theories engineered from a class of toric Calabi-Yau threefolds is explored. In previous work, we have argued for a triality structure by compiling evidence for the fact that every such manifold $X_{N,M}$ (for given $(N,M)$) engineers three a priori different, weakly coupled quiver gauge theories in five dimensions. The strong coupling regime of the latter is in general described by Little String Theories. Furthermore, we also conjectured that the manifold $X_{N,M}$ is dual to $X_{N^{\prime },M^{\prime }}$ if $NM=N^{\prime }{M}^{\prime }$ and $\text{gcd}(N,M)=\text{gcd}(N^{\prime },M^{\prime })$. Combining this result with the triality structure, we currently argue for a large number of dual quiver gauge theories, whose instanton partition functions can be computed explicitly as specific expansions of the topological partition function ${\mathcal{Z}}_{N,M}$ of $X_{N,M}$. We illustrate this web of dual theories by studying explicit examples in detail. We also undertake first steps in further analysing the extended moduli space of $X_{N,M}$ with the goal of finding other dual gauge theories.

43 Pages

References in corpus (5)

• The Refined Topological Vertex
• The Power of Nekrasov Functions
• Triality in Little String Theories
• Dual Little Strings and their Partition Functions
• M-theory on Elliptic Calabi-Yau Threefolds and 6d Anomalies

Cited by in corpus (10)

• Back to Heterotic Strings on ALE Spaces: Part I -- Instantons, 2-groups and T-duality
• From Little String Free Energies Towards Modular Graph Functions
• 3d Mirror Symmetry from S-duality
• Five-Dimensional Gauge Theories from Shifted Web Diagrams
• Dihedral Symmetries of Gauge Theories from Dual Calabi-Yau Threefolds
• Diagrammatic Expansion of Non-Perturbative Little String Free Energies
• Symmetric Orbifold Theories from Little String Residues
• $DE$-type little strings from glued brane webs
• Symmetries in A-Type Little String Theories, Part I
• A question on generalization of partition functions of CY 3-folds in String Theory