Toric Quiver Asymptotics and Mahler Measure: $\mathcal{N}=2$ BPS States

Abstract

BPS sector in $\mathcal{N}=2$, four-dimensional toric quiver gauge theories has previously been studied using crystal melting model and dimer model. We introduce the Mahler measure associated to statistical dimer model to study large $N$ limit of these quiver gauge theories. In this limit, generating function of BPS states in a general toric quiver theory is studied and entropy, growth rate of BPS states and free energy of the quiver are obtained in terms of the Mahler measure. Moreover, a possible third-order phase transition in toric quivers is discussed. Explicit computations of profile function, entropy density, BPS growth rate and phase structure of quivers are presented in concrete examples of clover ${\mathbb{C}}^3$, and resolved conifold $\mathcal{C}$ quivers. Finally, BPS growth rates of Hirzebruch ${\mathbb{F}}_0$, and ${\mathbb{C}}^3/{\mathbb{Z}}^2\times {\mathbb{Z}}^2$ orbifold quivers are obtained and a possible interpretation of the results for certain BPS black holes is discussed.

arXiv comment25 pages, 12 figures

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Cited by in corpus (5)

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• Mahler Measure for a Quiver Symphony
• Thermodynamics of Isoradial Quivers and Hyperbolic 3-Manifolds
• Reflexions on Mahler: Dessins, Modularity and Gauge Theories
• Functor of Points and Height Functions for Noncommutative Arakelov Geometry