From bosonic topological transition to symmetric fermion mass generation

A bosonic topological transition (BTT) is a quantum critical point between the bosonic symmetry-protected topological phase and the trivial phase. In this work, we investigate such a transition in a (2+1)-dimensional lattice model with the maximal microscopic symmetry: an internal SO(4) symmetry. We derive a description for this transition in terms of compact quantum electrodynamics (QED) with four fermion flavors (Nf=4). 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 Nf=2 noncompact 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 Nf=4 flavors of SU(2) fundamental fermions and one SU(2) fundamental Higgs boson. This provides a consistency check on both theories.