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Thermodynamics of Isoradial Quivers and Hyperbolic 3-Manifolds

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Ali Zahabi

High Energy Physics - Theory · Submitted 31 Dec 2019

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim As a result, we obtain the observables such as the BPS free energy, the BPS entropy density and growth rate of the isoradial quivers, as a function of the $R$-charges of the quiver and in terms of the hyperbolic volumes and the dilogarithm functions.

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arXiv ID1912.13245 (version 1)
Pith ID6EA4Y5NU, Pith's permanent record of this paper and its review
CitationAli Zahabi. "Thermodynamics of Isoradial Quivers and Hyperbolic 3-Manifolds." arXiv:1912.13245 (2019). https://pith.science/paper/6EA4Y5NU
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,881 input tokens.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.15 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.11 · compares with prior results 0.38 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

The BPS sector of $\mathcal{N}=2$, $4d$ toric quiver gauge theories, and its corresponding D6-D2-D0 branes on Calabi-Yau threefolds, have been previously studied using integrable lattice models such as the crystal melting model and the dimer model. The asymptotics of the BPS sector, in the large N limit, can be studied using the Mahler measure theory, \cite{Zah}. In this work, we consider the class of isoradial quivers and study their thermodynamical observables and phase structure. Building on our previous results, and using the relation between the Mahler measure and hyperbolic 3-manifolds, we propose a new approach in the asymptotic analysis of the isoradial quivers. As a result, we obtain the observables such as the BPS free energy, the BPS entropy density and growth rate of the isoradial quivers, as a function of the $R$-charges of the quiver and in terms of the hyperbolic volumes and the dilogarithm functions. The phase structure of the isoradial quivers is studied via the analysis of the BPS entropy density at critical $R$-charges and universal results for the phase structure in this class are obtained. Explicit results for the observables are obtained in some concrete examples of the isoradial quivers.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 The BPS sector of $\mathcal{N}=2$, $4d$ toric quiver gauge theories, and its corresponding D6-D2-D0 branes on Calabi-Yau threefolds, have been previously studied using integrable lattice models such as the crystal melting model and the dimer model. background 1.00 0.03 0.02 asserted 1.00
s1 The asymptotics of the BPS sector, in the large N limit, can be studied using the Mahler measure theory, \cite{Zah}. background 0.99 0.06 0.03 asserted 0.76
s2 In this work, we consider the class of isoradial quivers and study their thermodynamical observables and phase structure. contribution 1.00 0.70 0.06 asserted 0.91
s3 Building on our previous results, and using the relation between the Mahler measure and hyperbolic 3-manifolds, we propose a new approach in the asymptotic analysis of the isoradial quivers. method 0.59 0.68 0.09 asserted 0.75
s4 As a result, we obtain the observables such as the BPS free energy, the BPS entropy density and growth rate of the isoradial quivers, as a function of the $R$-charges of the quiver and in terms of the hyperbolic volumes and the dilogarithm functions. result 1.00 0.95 0.58 asserted 1.00
s5 The phase structure of the isoradial quivers is studied via the analysis of the BPS entropy density at critical $R$-charges and universal results for the phase structure in this class are obtained. result 0.66 0.93 0.26 asserted 1.00
s6 Explicit results for the observables are obtained in some concrete examples of the isoradial quivers. result 0.93 0.93 0.07 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.76 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

The BPS sector of $\mathcal{N}=2$, $4d$ toric quiver gauge theories, and its corresponding D6-D2-D0 branes on Calabi-Yau threefolds, have been previously studied using integrable lattice models such as the crystal melting model and the dimer model. The asymptotics of the BPS sector, in the large N limit, can be studied using the Mahler measure theory, \cite{Zah}. In this work, we consider the class of isoradial quivers and study their thermodynamical observables and phase structure. Building on our previous results, and using the relation between the Mahler measure and hyperbolic 3-manifolds, we propose a new approach in the asymptotic analysis of the isoradial quivers. As a result, we obtain the observables such as the BPS free energy, the BPS entropy density and growth rate of the isoradial quivers, as a function of the $R$-charges of the quiver and in terms of the hyperbolic volumes and the dilogarithm functions. The phase structure of the isoradial quivers is studied via the analysis of the BPS entropy density at critical $R$-charges and universal results for the phase structure in this class are obtained. Explicit results for the observables are obtained in some concrete examples of the isoradial quivers.

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3 arXiv papers cite this in 3 sentences

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Builds on 1 paper
  • The above mathematical result will be used in this article in the explicit computations of the Mahler measure of the NP of the isoradial quivers, and can be seen as the generalization of the results in [ref] .

    Mahler's Measure and the Dilogarithm (II) · Mahler Measure of Isoradial Quiver · 0.87

Cites as background 1 paper
  • Furthermore, as the isoradial quivers can be triangulated and they satisfy the gluing and completeness equations, their NP are similar to to A-polynomials and their closed cousines H-polynomials, for an introduction to A-polynomials and their Mahler measure see [ref] .

    An Introduction to A-polynomials and their Mahler Measures · NP of Isoradial Quiver and A-Polynomial · 0.99

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