A dual 2D model for the Quantum Hall Fluid

We present a dual two dimensional model for the Quantum Hall Fluid depending on two parameters and show that this model has topologically non-trivial vacua which are infrared stable fixed points of the Renormalization Group. The model has a discrete (modular) symmetry which reproduces the fenomenological law of corresponding states and allows for an unified description of the critical points corresponding to Hall plateaus in terms of a 2 dimensional Conformal Field Theory.Comment: 10 pages, Revtex, no figure

Paired states on a torus

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

A CFT description of the BTZ black hole: topology versus geometry (or thermodynamics versus statistical mechanics

In this paper we review the properties of the black hole entropy in the light of a general conformal field theory treatment. We find that the properties of horizons of the BTZ black holes in ADS_{3}, can be described in terms of an effective unitary CFT_{2} with central charge c=1 realized in terms of the Fubini-Veneziano vertex operators. It is found a relationship between the topological properties of the black hole solution and the infinite algebra extension of the conformal group in 2D, SU(2,2), i.e. the Virasoro Algebra, and its subgroup SL(2,Z) which generates the modular symmetry. Such a symmetry induces a duality for the black hole solution with angular momentum J\neq 0. On the light of such a global symmetry we reanalyze the Cardy formula for CFT_{2} and its possible generalization to D>2 proposed by E. Verlinde.Comment: 21 page

The Cardy-Verlinde equation in a spherical symmetric gravitational collapse

The Cardy-Verlinde formula is analyzed in the contest of the gravitational collapse. Starting from the holographic principle, we show how the equations for a homogeneous and isotropic gravitational collapse describe the formation of the black hole entropy. Some comments on the role of the entangled entropy and the connection with the c-theorem are made

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

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

The global phase diagram of a modular invariant two dimensional statistical model

A generalization of the Coulomb Gas model with modular SL(2, Z)-symmetry allows for a discrete infinity of phases which are characterized by the condensation of dyonic pseudoparticles and the breaking of parity and time reversal. Here we study the phase diagram of such a model by using renormalization group techniques. Then the symmetry SL(2,Z) acting on the two-dimensional parameter space gives us a nested shape of its global phase diagram and all the infrared stable fixed points. Finally we propose a connection with the 2-dimensional Conformal Field Theory description of the Fractional Quantum Hall Effect.Comment: 17 pages LaTeX + 1 figur

Schwinger Model Green functions with topological effects

The fermion propagator and the 4-fermion Green function in the massless QED2 are explicitly found with topological effects taken into account. The corrections due to instanton sectors k=+1,-1, contributing to the propagator, are shown to be just the homogenous terms admitted by the Dyson-Schwinger equation for S. In the case of the 4-fermion function also sectors k=+2,-2 are included into consideration. The quark condensates are then calculated and are shown to satisfy cluster property. The theta-dependence exhibited by the Green functions corresponds to and may be removed by performing certain chiral gauge transformation.Comment: 16 pages, in REVTE

Cortico-cortical stimulation and robot-assisted therapy (CCS and RAT) for upper limb recovery after stroke: study protocol for a randomised controlled trial

Background: Since birth, during the exploration of the environment to interact with objects, we exploit both the motor and sensory components of the upper limb (UL). This ability to integrate sensory and motor information is often compromised following a stroke. However, to date, rehabilitation protocols are focused primarily on recovery of motor function through physical therapies. Therefore, we have planned a clinical trial to investigate the effect on functionality of UL after a sensorimotor transcranial stimulation (real vs sham) in add-on to robot-assisted therapy in the stroke population. Methods: A randomised double-blind controlled trial design involving 32 patients with a single chronic stroke (onset > 180 days) was planned. Each patient will undergo 15 consecutive sessions (5 days for 3 weeks) of paired associative stimulation (PAS) coupled with UL robot-assisted therapy. PAS stimulation will be administered using a bifocal transcranial magnetic stimulator (TMS) on the posterior-parietal cortex and the primary motor area (real or sham) of the lesioned hemisphere. Clinical, kinematics and neurophysiological changes will be evaluated at the end of protocol and at 1-month follow-up and compared with baseline. The Fugl-Meyer assessment scale will be the primary outcome. Secondly, kinematic variables will be recorded during the box-and-block test and reaching tasks using video analysis and inertial sensors. Single pulse TMS and electroencephalography will be used to investigate the changes in local cortical reactivity and in the interconnected areas. Discussion: The presented trial shall evaluate with a multimodal approach the effects of sensorimotor network stimulation applied before a robot-assisted therapy training on functional recovery of the upper extremity after stroke. The combination of neuromodulation and robot-assisted therapy can promote an increase of cortical plasticity of sensorimotor areas followed by a clinical benefit in the motor function of the upper limb. Trial registration: ClinicalTrials.gov NCT05478434. Registered on 28 Jul 2022