high-energy physics

Interior zeros of supersymmetric indices

arXiv:2607.28143

summary

The paper investigates interior zeros of supersymmetric indices, showing they arise when underlying arithmetic coefficients grow exponentially and can be identified from the q‑series expansion, affecting infrared descriptions of 4d N=1 SU(2) SQCD and revealing finite‑N effects in the N=4 U(N) Schur index via giant graviton expansions.

Abstract

A supersymmetric index has interior zeros ( $∣ q ∣ < 1$ ) if and only if the arithmetic coefficients $I^´ (I^½)$ underlying the supersymmetric zeta function grow exponentially at a rate set by the nearest zero. Each $I^´ (I^½)$ 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 $N = 1$ $S U (2)$ 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.

8 pages, 2 figures

Topics & keywords

#supersymmetric index #interior zeros #q-series #gauge theory #giant gravitonssupersymmetric indexinterior zerosq-series coefficientsSU(2) SQCDN=4 U(N) Schur indexgiant graviton expansion