  In contemporary physics, especially in condensed matter physics, fermionic
topological order and its protected edge modes are one of the most important
objects. In this work, we propose a systematic construction of the cylinder
partition corresponding to the fermionic fractional quantum Hall effect (FQHE)
and a general mechanism for obtaining the candidates of the protected edge
modes. In our construction, when the underlying conformal field theory has the
$Z_{2}$ duality defects corresponding to the fermionic $Z_{2}$ electric
particle, we show that the FQH partition function has a fermionic T duality.
This duality is analogous to (hopefully the same as) the dualities in the dual
resonance models, typically known as supersymmetry, and gives a renormalization
group (RG) theoretic understanding of the topological phases. We also introduce
a modern understanding of bulk topological degeneracies and topological
entanglement entropy. This understanding is based on the traditional tunnel
problem and the recent conjecture of correspondence between the bulk
renormalization group flow and the boundary conformal field theory. Our
formalism gives an intuitive and general understanding of the modern physics of
the topologically ordered systems in the traditional language of RG and
fermionization.
