Beyond Triality: Dual Quiver Gauge Theories and Little String Theories

TL;DR

This paper explores dualities among quiver gauge theories derived from toric Calabi-Yau threefolds, revealing a complex web of triality and duality structures that connect different theories and their strong coupling limits described by Little String Theories.

Contribution

It introduces a new duality framework extending triality to a larger set of quiver gauge theories associated with toric Calabi-Yau manifolds, and relates their partition functions to topological string computations.

Findings

Identification of dual quiver gauge theories for given Calabi-Yau manifolds.

Explicit computation of instanton partition functions via topological string expansions.

Evidence supporting a generalized duality structure beyond triality.

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 $X_{N',M'}$ if $NM=N'M'$ and $\text{gcd}(N,M)=\text{gcd}(N',M')$. 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.