Superconformal index of N=3 orientifold theories

TL;DR

This work computes the superconformal index for ${\cal N}=3$ $\mathbb{Z}_k$ orientifold theories in the large-$N$ limit by projecting the KK spectrum of type IIB supergravity on $\mathrm{AdS}_5\times S^5/\mathbb{Z}_k$. Using an extended index with a $U(1)_Y$ fugacity, the authors implement the $\mathbb{Z}_k$ projection to obtain $I^{\rm KK}_{\mathbb{Z}_k}$, showing agreement with known ${\cal N}=4$ cases at $k=2$ and revealing genuine ${\cal N}=3$ content for $k=3,4,6$ through the surviving KK modes and Coulomb-branch operators of dimension $k$. Finite-$N$ corrections are analyzed via wrapped D3-branes and discrete torsions, with the leading $O(N)$ corrections depending on the torsion data and the topology of the internal space, producing positive or negative contributions to the index. The results illuminate how discrete torsion controls non-perturbative operator content and baryonic/wrapped-brane contributions, offering holographic insight into the BPS spectrum and domain-wall structures of ${\cal N}=3$ theories.

Abstract

We analyze the superconformal index of the N=3 supersymmetric Z_k generalized orientifold theories recently proposed. In the large N limit we derive the index from the Kaluza-Klein modes in AdS_5 x S^5/Z_k, which are obtained from ones in AdS_5 x S^5 by a simple projection. For the ordinary Z_2 orientifold case the agreement with the gauge theory calculation is explicitly confirmed, and for Z_k with k > 2 we perform a few consistency checks with known results for N=3 theories. We also study finite N corrections by analyzing wrapped D3-branes and discrete torsions in the dual geometry.