Large-N limit of chiral quiver theories: free energy, supersymmetric indices and operator counting
Abstract
We find the first analytic solution to the large-N saddle point equations for the S3 free energy of a chiral 𝒩=2 Chern-Simons-matter theory with an M-theory dual. Focusing on the chiral quiver dual to AdS4× Q1,1,1/ℤk, we show how the long-range forces of the matrix model cancel at large N, resolving a long-standing tension with the expected N3/2 scaling. The resulting free energy precisely matches the holographic prediction for all assignments of trial R-charges. Our results extend to the superconformal and topologically twisted indices on S2× S1, whose large-N and Cardy limit is determined by the same saddle. The solution agrees with the predictions of the operator counting method, giving strong evidence for this conjecture beyond non-chiral quivers. We support the analytic solution with a finite-N numerical analysis for multiple assignments of R-charges, extending recent numerical results obtained for this quiver.
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BibTeX
@misc{colombo2026largen,
title = {{Large-$N$ limit of chiral quiver theories: free energy, supersymmetric indices and operator counting}},
author = {Edoardo Colombo and Hyojoong Kim and Nakwoo Kim and Hoseob Shin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.39569},
eprint = {2610.39569},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.39569},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Large-N limit of chiral quiver theories: free energy, supersymmetric indices and operator counting
AU - Edoardo Colombo
AU - Hyojoong Kim
AU - Nakwoo Kim
AU - Hoseob Shin
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.39569
UR - https://arxiv.org/abs/2610.39569
AB - We find the first analytic solution to the large-N saddle point equations for the S^3 free energy of a chiral 𝒩=2 Chern-Simons-matter theory with an M-theory dual. Focusing on the chiral quiver dual to AdS_4× Q^1,1,1/ℤ_k, we show how the long-range forces of the matrix model cancel at large N, resolving a long-standing tension with the expected N^3/2 scaling. The resulting free energy precisely matches the holographic prediction for all assignments of trial R-charges. Our results extend to the superconformal and topologically twisted indices on S^2× S^1, whose large-N and Cardy limit is determined by the same saddle. The solution agrees with the predictions of the operator counting method, giving strong evidence for this conjecture beyond non-chiral quivers. We support the analytic solution with a finite-N numerical analysis for multiple assignments of R-charges, extending recent numerical results obtained for this quiver.
ER -