Universal transport theory for paired fractional quantum Hall states in the quantum point contact geometry

Even-denominator fractional quantum Hall (FQH) states can be viewed as topological superconductors of composite fermions, supporting a charged chiral mode and |Ccf| neutral Majorana modes set by the Chern number Ccf. Despite ongoing efforts, distinguishing the many competing paired phases remains an open problem. In this work, we propose a unified theory of charge transport across a quantum point contact (QPC) for general paired FQH states described by an so(N)₁ × u(1) conformal field theory. We derive the boundary effective action for an arbitrary number of Majorana fermions N=|Ccf| and develop a non-perturbative instanton approximation to describe tunneling processes. We establish a weak-strong duality relating strong quasiparticle tunneling to weak electron tunneling. We calculate the scaling dimensions of the tunneling operators and demonstrate that while the weak-coupling fixed point is generally unstable, the strong-coupling fixed point is stable for physically relevant filling fractions and number of Majorana fermions. These transport exponents provide a distinct experimental fingerprint to identify the topological phases of even-denominator FQH states.