Topological holography for fermions

TL;DR

This paper extends topological holography to fermionic systems, providing a unified framework to classify, analyze, and discover new fermionic topological phases and critical points using symmetry topological field theories.

Contribution

It introduces a fermionic SymTFT framework that captures known properties of fermionic SPT phases and enables the discovery of new fermionic gapless phases with emergent anomalies.

Findings

Classified 1+1D fermionic gapped phases and critical points.

Reproduced properties of fermionic SPT phases, including edge modes and stacking rules.

Constructed a new intrinsically gapless fermionic SPT phase with emergent fermionic anomaly.

Abstract

Topological holography is a conjectured correspondence between the symmetry charges and defects of a $D$-dimensional system with the anyons in a $(D+1)$-dimensional topological order: the symmetry topological field theory (SymTFT). Topological holography is conjectured to capture the topological aspects of symmetry in gapped and gapless systems, with different phases corresponding to different gapped boundaries (anyon condensations) of the SymTFT. This correspondence was previously considered primarily for bosonic systems, excluding many phases of condensed matter systems involving fermionic electrons. In this work, we extend the SymTFT framework to establish a topological holography correspondence for fermionic systems. We demonstrate that this fermionic SymTFT framework captures the known properties of $1+1D$ fermion gapped phases and critical points, including the classification, edge-modes, and stacking rules of fermionic symmetry-protected topological phases (SPTs), and computation of partition functions of fermionic conformal field theories (CFTs). Beyond merely reproducing known properties, we show that the SymTFT approach can additionally serve as a practical tool for discovering new physics, and use this framework to construct a new example of a fermionic intrinsically gapless SPT phase characterized by an emergent fermionic anomaly.