# Baryonic Supersymmetry in the Cheng-Yuan model

We study the Baryonic Supersymmetry (BST) in the Cheng-Yuan model by using the BST-like space-time as a model of the CFT$_2$ and the $\mathbb{Z}_2$ gauge theory. We start from a 4D CFT$_2$ model with $T=\mathbb{Z}_2$ and observe that the BST-like space-time is a perturbative space-time with the boundary as a boundary which has a Bunch-Davies semisimple basis. We provide detailed calculations of the BST-like space-time as a model of the $\mathbb{Z}_2$-CFT$_2$ model and find that it is a small enough world for the deterministic Bunch-Davies semisimple basis. We also show that the Bunch-Davies semisimple basis is a non-perturbative representation of the Leibnitz basis, which is a non-perturbative field theory. Finally, we consider the problem of the Bunch-Davies semisimple basis and find that it is a non-perturbative representation of the Lorenz basis, which is a non-perturbative field theory.