Quiver superconformal index and giant gravitons: asymptotics and expansions
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arXiv
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| Natura: | Preprint |
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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 |