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

We note an implication of 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 non-universality of the edge exponent implies non-universality of the Hall conductance, as measured in the two-terminal conductance.