Universality lost: Relation between quantizations of the Hall conductance and the edge exponents in fractional quantum Hall effect

We note an implication of the chiral Luttinger liquid based edge state description of the fractional quantum Hall effect. By considering several examples that involve backward moving neutral modes, arising from either composite fermions with reverse flux attached or edge reconstruction, we show that nonuniversality of the edge exponent implies nonuniversality of the Hall conductance, as measured in the two-terminal conductance.