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arXiv · 2607.28143

Interior zeros of supersymmetric indices

Yu Nakayama·Tadashi Okazaki
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Abstract

A supersymmetric index has interior zeros ($|q|<1$) if and only if the arithmetic coefficients $\delta(\nu)$ underlying the supersymmetric zeta function grow exponentially at a rate set by the nearest zero. Each $\delta(\nu)$ follows from finitely many $q$-series coefficients, so interior zeros are detectable from the expansion alone and obstruct a free or s-confining infrared description, as we show for 4d $\mathcal{N}=1$ $SU(2)$ SQCD. With a giant graviton expansion interior zeros are a finite $N$ effect, located by the energy of one giant graviton, verified for the $\mathcal{N}=4$ $U(N)$ Schur index.

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Yu Nakayama, Tadashi Okazaki. 2026-07-30. Interior zeros of supersymmetric indices. https://arxiv.org/abs/2607.28143

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