A Holographic Theory for the Phase Transitions Between Fermionic Symmetry-protected Topological States

In an earlier work we developed a holographic theory for the phase transition between bosonic symmetry-protected topological (SPT) states. This paper is a continuation of it. Here we present the holographic theory for fermionic SPT phase transitions. We show that in any dimension $d$, the critical states of fermionic SPT phase transitions has an emergent $Z_2^T$ symmetry and can be realized on the boundary of a $d+1$-dimensional bulk SPT with an extra $Z_2^T$ symmetry.