  We propose an effective field theory (EFT) of fractional quantum Hall systems
near the filling fraction $\nu=5/2$ that flows to pertinent IR candidate
phases, including non-abelian Pfaffian, anti-Pfaffian, and particle-hole
Pfaffian states (Pf, APf, and PHPf). Our EFT has a 2+1$d$ O(2)$_{2,L}$
Chern-Simons gauge theory coupled to four Majorana fermions by a discrete
charge conjugation gauge field, with Gross-Neveu-Yukawa-Higgs terms. Including
deformations via a Higgs condensate and fermion mass terms, we can map out a
phase diagram with tunable parameters, reproducing the prediction of the
recently-proposed percolation picture and its gapless topological quantum phase
transitions. Our EFT captures known features of both gapless and gapped sectors
of time-reversal-breaking domain walls between Pf and APf phases. Moreover, we
find that Pf$\mid$APf domain walls have higher tension than domain walls in the
PHPf phase. Then the former, if formed, may transition to the
energetically-favored PHPf domain walls; this could, in turn, help further
induce a bulk transition to PHPf.
