Abstract
Fractional quantum Hall (FQH) system at Landau level filling fraction ν=5/2 has long been suggested to be non-Abelian, either Pfaffian (Pf) or antiPfaffian (APf) states by numerical studies, both with quantized Hall conductance σ_xy=5e²/2h. Thermal Hall conductances of the Pf and APf states are quantized at κ_xy=7/2 and κ_xy=3/2 respectively in a proper unit. However, a recent experiment shows the thermal Hall conductance of ν=5/2 FQH state is κ_xy=5/2. It has been speculated that the system contains random Pf and APf domains driven by disorders, and the neutral chiral Majorana modes on the domain walls may undergo a percolation transition to a κ_xy=5/2 phase. In this work, we do perturbative and non-perturbative analyses on the domain walls between Pf and APf. We show the domain wall theory possesses an emergent SO(4) symmetry at energy scales below a threshold Λ₁, which is lowered to an emergent U(1)×U(1) symmetry at energy scales between Λ₁ and a higher value Λ₂, and is finally lowered to the composite fermion parity symmetry Z₂^F above Λ₂. Based on the emergent symmetries, we propose a phase diagram of the disordered ν=5/2 FQH system, and show that a κ_xy=5/2 phase arises at disorder energy scales Λ>Λ₁. Furthermore, we show the gapped double-semion sector of N_D compact domain walls contributes non-local topological degeneracy 2^N_D-1, causing a low-temperature peak in the heat capacity. We implement a non-perturbative method to bootstrap generic topological 1+1D domain walls (2-surface defects) applicable to any 2+1D non-Abelian topological order. We identify potentially relevant spin TQFTs for various ν = 5/2 FQH states in terms of fermionic version of U(1)_± 8 Chern-Simons theory × Z₈-class TQFTs.