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 identify the impurity interactions of the recently proposed CFT description of a bilayer Quantum Hall system at filling ν = m pm+2[1]. Such a CFT is obtained by m-reduction on the one layer system, with a resulting pairing symmetry and presence of quasi-holes. For the m = 2 case boundary terms are shown to describe an impurity interaction which allows for a localized tunnel of the Kondo problem type.The presence of an anomalous fixed point is evidenced at finite coupling which is unstable with respect to unbalance and flows to a vacuum state with no quasi-holes.

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.

We analyze the modular properties of the effective CFT description for Jain plateaux, proposed in [1], corresponding to the fillings ν = m 2pm+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 the partition function go to complete a Z m -orbifold construction of the RCFT u(1)× su(m) 1 proposed for the Jain states [2,3]. The resulting extended algebra of the chiral primary fields can be also viewed as a RCFT extension of the u(1)×W m minimal models [3]. For m = 2 we prove that our model, the TM, gives the RCFT closure of the extended minimal models u(1)×W 2 .

We show how the recently proposed effective theory for a Quantum Hall system at "paired states" filling ν = 1 [1][2], the twisted model (TM), well adapts to describe the phenomenology of Josephson Junction ladders (JJL) in the presence of defects. In particular it is shown how naturally the phenomenon of flux fractionalization takes place in such a description and its relation with the discrete symmetries present in the TM. Furthermore we focus on "closed" geometries, which enable us to analyze the topological properties of the ground state of the system in relation to the presence of half flux quanta.

The characteristic sizes of astrophysical structures, up to the whole observed Universe, can be recovered, in principle, assuming that gravity is the overall interaction assembling systems starting from microscopic scales, whose order of magnitude is ruled by the Planck length and the related Compton wavelength. This result agrees with the absence of screening mechanisms for the gravitational interaction and could be connected to the presence of Yukawa corrections in the Newtonian potential which introduce typical interaction lengths. This result directly comes out from quantization of primordial black holes and then characteristic interaction lengths directly emerge from quantum field theory.PACS numbers: 04.50.+h, 95.36.+x, 98.80.-k

We show how the recently proposed CFT for a bilayer Quantum Hall system at filling ν = m pm+2 [1]−[3], the Twisted Model (TM), is equivalent to the system of two massless scalar bosons with a magnetic boundary interaction as introduced in [4], at the so called "magic" points. We are then able to describe, within such a framework, the dissipative quantum mechanics of a particle confined to a plane and subject to an external magnetic field normal to it. Such an analogy is further developed in terms of the TM boundary states, by describing the interaction between an impurity with a Hall system.