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

## TL;DR

This paper extends holographic theories to describe phase transitions between fermionic symmetry-protected topological states, revealing emergent symmetries at critical points and their realization on higher-dimensional boundaries.

## Contribution

It introduces a holographic framework for fermionic SPT phase transitions, building upon previous work on bosonic states, and identifies emergent symmetries at criticality.

## Key findings

- Critical states exhibit emergent Z2^T symmetry.
- Critical states can be realized on the boundary of a higher-dimensional bulk SPT.
- The theory applies across any spatial dimension d.

## Abstract

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.