We extend the construction of the effective conformal field theory for the Jain hierarchical fillings proposed in [7] to the description of a quantum Hall fluid at non standard fillings ν = m pm+2 . The chiral primary fields are found by using a procedure which induces twisted boundary conditions on the m scalar fields; they appear as composite operators of a charged and neutral component. The neutral modes describe parafermions and contribute to the ground state wave function with a generalized Pfaffian term. Correlators of N e electrons in the presence of quasi-hole excitations are explicitly given for m = 2.

We analyze the modular properties of the effective CFT description for paired states, proposed in cond-mat/0003453, corresponding to the non-standard filling nu =1/(p+1). We construct its characters for the twisted and the untwisted sector and the diagonal partition function. We show that the degrees of freedom entering our partition function naturally go to complete a Z_2-orbifold construction of the CFT for the Halperin state. Different behaviours for the p even and p odd cases are also studied. Finally it is shown that the tunneling phenomenon selects out a twist invariant CFT which is identified with the Moore-Read model.Comment: 24 pages, 1 figure, Late

We construct an effective conformal field theory by using a procedure which induces twisted boundary conditions for the fundamental scalar fields. That allows one to describe a quantum Hall fluid at Jain hierarchical filling, ν = m 2pm+1 , in terms of one charged scalar field and m − 1 neutral ones. Then the resulting algebra of the chiral primary fields is U(1) × Wm. Finally the ground state wave functions are given as correlators of appropriate composite fields (a-electrons). 547 Mod. Phys. Lett. A 2000.15:547-555. Downloaded from www.worldscientific.com by UNIVERSITY OF CALIFORNIA @ SAN DIEGO on 02/04/15. For personal use only.