Quiver superconformal index and giant gravitons: asymptotics and expansions

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Autori principali: Purkayastha, Souradeep, Qu, Zishen, Zahabi, Ali
Natura: Preprint
Pubblicazione: 2025
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author Purkayastha, Souradeep
Qu, Zishen
Zahabi, Ali
author_facet Purkayastha, Souradeep
Qu, Zishen
Zahabi, Ali
contents We study asymptotics of the $d=4$, $\mathcal{N}=1$ superconformal index for toric quiver gauge theories. Using graph-theoretic and algebraic factorization techniques, we obtain a cycle expansion for the large-$N$ index in terms of the $R$-charge-weighted adjacency matrix. Applying saddle-point techniques at the on-shell $R$-charges, we determine the asymptotic degeneracy in the univariate specialization for $\hat{A}_{m}$, and along the main diagonal for the bivariate index for $\mathcal{N}=4$ and $\hat{A}_{3}$. In these cases we find $\ln |c_{n}| \sim γn^{\frac{1}{2}}+ β\ln n + α$ (Hardy-Ramanujan type). We also identify polynomial growth for $dP3$, $Y^{3,3}$ and $Y^{p,0}$, and give numerical evidence for $γ$ in further $Y^{p,p}$ examples. Finally, we generalize Murthy's giant graviton expansion via the Hubbard-Stratonovich transformation and Borodin-Okounkov formula to multi-matrix models relevant for quivers.
format Preprint
id arxiv_https___arxiv_org_abs_2509_12123
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Quiver superconformal index and giant gravitons: asymptotics and expansions
Purkayastha, Souradeep
Qu, Zishen
Zahabi, Ali
High Energy Physics - Theory
Mathematical Physics
Combinatorics
We study asymptotics of the $d=4$, $\mathcal{N}=1$ superconformal index for toric quiver gauge theories. Using graph-theoretic and algebraic factorization techniques, we obtain a cycle expansion for the large-$N$ index in terms of the $R$-charge-weighted adjacency matrix. Applying saddle-point techniques at the on-shell $R$-charges, we determine the asymptotic degeneracy in the univariate specialization for $\hat{A}_{m}$, and along the main diagonal for the bivariate index for $\mathcal{N}=4$ and $\hat{A}_{3}$. In these cases we find $\ln |c_{n}| \sim γn^{\frac{1}{2}}+ β\ln n + α$ (Hardy-Ramanujan type). We also identify polynomial growth for $dP3$, $Y^{3,3}$ and $Y^{p,0}$, and give numerical evidence for $γ$ in further $Y^{p,p}$ examples. Finally, we generalize Murthy's giant graviton expansion via the Hubbard-Stratonovich transformation and Borodin-Okounkov formula to multi-matrix models relevant for quivers.
title Quiver superconformal index and giant gravitons: asymptotics and expansions
topic High Energy Physics - Theory
Mathematical Physics
Combinatorics
url https://arxiv.org/abs/2509.12123