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Quiver Asymptotics: $\mathcal{N}=1$ Free Chiral Ring

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arxiv 1811.11229 v2 pith:OMROKFRN submitted 2018-11-27 hep-th math-phmath.MP

classification hep-thmath-phmath.MP
keywords quiverasymptoticschiralcountinglargemathcalmatrixobtained
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abstract

The large N generating functions for the counting of chiral operators in $\mathcal{N}=1$, four-dimensional quiver gauge theories have previously been obtained in terms of the weighted adjacency matrix of the quiver diagram. We introduce the methods of multi-variate asymptotic analysis to study this counting in the limit of large charges. We describe a Hagedorn phase transition associated with this asymptotics, which refines and generalizes known results on the 2-matrix harmonic oscillator. Explicit results are obtained for two infinite classes of quiver theories, namely the generalized clover quivers and affine $\mathbb{C}^3/\hat{A}_n$ orbifold quivers.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Critical dimensions and small cycle dominance from all-orders asymptotics of $d$-matrix theory

    hep-th 2026-03 conditional novelty 7.0 of 10

    The weighted partition numbers of d-matrix theory admit an all-orders asymptotic expansion that switches from divergent to convergent at d=13 (bosonic) or 7 (fermionic).

  2. Negative heat capacities in spherically symmetric sectors of $d$-matrix quantum mechanics

    hep-th 2026-06 unverdicted novelty 6.0 of 10

    SO(d) and O(d) invariant sectors of d-matrix QM show negative microcanonical heat capacity that becomes positive at k_crit ~ N^2/4, forming a caloric fold similar to AdS black holes.

  3. Quiver superconformal index and giant gravitons: asymptotics and expansions

    hep-th 2025-09 conditional novelty 6.0 of 10

    For toric quiver theories, coefficients of the large-N superconformal index grow like exp(constant*sqrt(n)) times n^((m-5)/4) for the A-hat_m family, with polynomial growth for dP3 and Y^{p,0}.

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