From Bosonic Topological Transition to Symmetric Fermion Mass Generation

TL;DR

This paper develops a quantum electrodynamics framework with four fermion flavors to describe the bosonic topological transition, linking it to symmetric fermion mass generation and providing a unified theoretical perspective.

Contribution

It introduces a lattice model description of the BTT with maximal SO(4) symmetry using compact QED with four fermion flavors, and connects it to symmetric mass generation theories.

Findings

Identifies the critical point with emergent O(4) symmetry.

Recovers previous Nf=2 QED description by symmetry reduction.

Links BTT to symmetric mass generation via merging two transitions.

Abstract

The bosonic topological transition (BTT) is a quantum critical point between the bosonic symmetry protected topological phase and the trivial phase. In this work, we derive a description of this transition in terms of compact quantum electrodynamics (QED) with four fermion flavors ($N_f=4$). This allows us to describe the transition in a lattice model with the maximal microscopic symmetry: an internal SO(4) symmetry. Within a systematic renormalization group analysis, we identify the critical point with the desired O(4) emergent symmetry and all expected deformations. By lowering the microscopic symmetry we recover the previous $N_f=2$ non-compact QED description of the BTT. Finally, by merging two BTTs we recover a previously discussed theory of symmetric mass generation, as an SU(2) quantum chromodynamics-Higgs theory with $N_f=4$ flavors of SU(2) fundamental fermions and one SU(2) fundamental Higgs boson. This provides a consistency check on both theories.