Jain states on a torus: an unifying description

We analyze the modular properties of the effective CFT description for Jain plateaux corresponding to the fillings nu=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)xSU(m)$ proposed for the Jain states. The resulting extended algebra of the chiral primary fields can be also viewed as a RCFT extension of the U(1)xW(m) minimal models. For m=2 we prove that our model, the TM, gives the RCFT closure of the extended minimal models U(1)xW(2).Comment: 27 pages, Latex, JHEP style, no figure

Tunnelling Effects in a Brane System and Quantum Hall Physics

We argue that a system of interacting D-branes, generalizing a recent proposal, can be modelled as a Quantum Hall fluid. We show that tachyon condensation in such a system is equivalent to one particle tunnelling. In a conformal field theory effective description, that induces a transition from a theory with central charge c=2 to a theory with c=3/2, with a corresponding symmetry enhancement.Comment: 12 pages, no figures, Latex, some aspects clarified, sect.3 expanded, references adde

T-Dualities and Doubled Geometry of the Principal Chiral Model

The Principal Chiral Model (PCM) defined on the group manifold of SU(2) is here investigated with the aim of getting a further deepening of its relation with Generalized and Doubled Geometry. A one-parameter family of equivalent Hamiltonian descriptions is introduced, and cast into the form of Born geometries. Then O(3,3) duality transformations of the target phase space are performed and we show that the resulting dual models are defined on the group SB(2,C) which is the Poisson-Lie dual of SU(2) in the Iwasawa decomposition of the Drinfel'd double SL(2, C). Moreover, starting from the Lagrangian approach, a new kind of duality is found between the SU(2) PCM and the natural one defined on SB(2,C) which is not an isometry of the target phase space. A parent action with doubled degrees of freedom and configuration space SL(2, C) is then defined that reduces to either one of the dually related models, once suitable constraints are implemented.Comment: 41 pages, revised version published in JHE

A conformal field theory description of the paired and parafermionic states in the quantum Hall effect

We extend the construction of the effective conformal field theory for the Jain hierarchical fillings proposed in cond-mat/9912287 to the description of a quantum Hall fluid at non standard fillings nu=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 Ne electrons in the presence of quasi-hole excitations are explicitly given for m=2.Comment: 11 pages, plain Late

Transport properties in bilayer Quantum Hall systems in the presence of a topological defect

Following a suggestion given in Phys. Lett. B 571(2003) 621, we show how a bilayer Quantum Hall system at fillings nu =1/p+1 can exhibit a point-like topological defect in its edge state structure. Indeed our CFT theory for such a system, the Twisted Model (TM), gives rise in a natural way to such a feature in the twisted sector. Our results are in agreement with recent experimental findings (Phys. Rev. B 72 (2005) 041305) which evidence the presence of a topological defect in the transport properties of the bilayer system.Comment: 10 pages, 4 figures; talk given by A. Naddeo at "X Training Course in the Physics of Correlated Electron Systems and High-Tc Superconductors, Vietri sul Mare (SA),Italy, 3-14 October 200

A twisted conformal field theory description of the Quantum Hall Effect

We construct an effective conformal field theory by using a procedure which induces twisted boundary conditions for the fundamental scalar fields. That allows to describe a quantum Hall fluid at Jain hierarchical filling, nu=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)xW_m. Finally the ground state wave functions are given as correlators of appropriate composite fields (a-electrons).Comment: 11 pages, plain Late

Twisted CFT and bilayer Quantum Hall systems

We identify the impurity interactions of the recently proposed CFT description of a bilayer Quantum Hall system at filling nu =m/(pm+2) in Mod. Phys. Lett. A 15 (2000) 1679. 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.Comment: 15 pages, 1 figure, Late