5d superconformal indices at large N and holography

TL;DR

This work addresses computing the perturbative large-$N$ superconformal index for 5d ${\cal N}=1$ quiver fixed points with $AdS_6\times S^4/\mathbb{Z}_n$ duals. It proposes a general orbifold prescription: start from the USp(2N) parent theory, project onto orbifold-invariant states, and add twisted-sector contributions, yielding $\mathcal{I}_n = \mathrm{PE}[G_n]$ with $G_n = \frac{1}{n}\sum_{j=0}^{n-1} G_1(\omega^j z) + (n-1)\Delta$, $\Delta = \frac{x^2}{(1-xy)(1-xy^{-1})}$. The authors perform explicit large-$N$ checks for ${\\mathbb{Z}}_2$ and ${\\mathbb{Z}}_3$ orbifolds, finding identical indices for the two even ${\\mathbb{Z}}_2$ theories and agreement with gravity expectations, including operator mappings of twisted and untwisted sectors. These results reinforce the AdS/CFT picture for 5d quivers and point to future work on instanton contributions and symmetry enhancements in the index.

Abstract

We propose a general formula for the perturbative large N superconformal index of 5d quiver fixed point theories that have an AdS(6)xS(4)/Z(n) supergravity dual. This index is obtained from the parent theory by projecting to orbifold-invariant states and adding the twisted sector contributions. Our result agrees with expectations from the dual supergravity description. We test our formula against the direct computation of the index for Z(2) and Z(3) and find complete agreement.