Suspended Fixed Points

We study the orientifold of the ${\mathcal{N}} = 1$ superconformal field theories describing D3-branes probing the Suspended Pinch Point singularity, as well as the orientifolds of non-chiral theories obtained by a specific orbifold $\mathbb{Z}_n$ of SPP. We find that these models realize a mechanism analogous to the one recently found for the orientifold of the complex Calabi-Yau cone over the Pseudo del Pezzo surface PdP$_{3c}$: they all flow to a new IR fixed point such that the value of the $a$-charge is less than half the one of the oriented theory. We also find that the value of $a$ coincides with the charge of specific orientifolds of the toric singularities $L^{(\bar{n},\bar{n},\bar{n})}$ with $\bar{n}=3n/2$ for $n$ even or $L^{(\bar{n},\bar{n}+1,\bar{n})}$ with $\bar{n}=(3n{-}1)/2$ for $n$ odd, suggesting the existence of an IR duality.