Interior zeros of supersymmetric indices

2026/07/30 by Yu Nakayama, Tadashi Okazaki
Physics and Astronomy · #hep-th

paper · pdf

8 pages, 2 figures

arxiv created 2026/07/30 · arxiv updated 2026/07/31

Abstract

A supersymmetric index has interior zeros (|q|<1) if and only if the arithmetic coefficients δ(ν) underlying the supersymmetric zeta function grow exponentially at a rate set by the nearest zero. Each δ(ν) 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 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 N=4 U(N) Schur index.

Citations

• Supersymmetric zeta functions and determinants
• The Superconformal Index and Black Hole Instabilities
• Giant graviton expansion of Schur index and quasimodular forms
• Analytic continuation for giant gravitons
• Unitary matrix models, free fermion ensembles, and the giant graviton expansion
• The exact Schur index in closed form
• The Giant Graviton Expansion
• Finite-N superconformal index via the AdS/CFT correspondence
• Zeros of the deformed exponential function
• On certain class of entire functions and a conjecture by Alan Sokal
• Modular operads

Related

• Large N Schur index of \mathcal N=4 SYM from semiclassical D3 brane
• The Superconformal Index and Black Hole Instabilities
• Giant graviton expansion of Schur index and quasimodular forms
• Supersymmetric zeta functions and determinants
• Why Indices Count the Total Number of Black Hole Microstates (at large N)