A Unifying Conformal Field Theory Approach to the Quantum Ha(2)

We review the main results of the effective description of the Quantum Hall fluid for the Jain fillings, nu=m/2pm+1, and the non-standard ones nu=m/pm+2 by a conformal field theory (CFT) in two dimensions. It is stressed the unifying character of the m-red

ABSTRACT

Wereviewthemainresultsofthee ectivedescriptionoftheQuantumHall uidfor

byaconformal eldtheJain llings,ν=m

pm+2theory(CFT)intwodimensions.Itisstressedtheunifyingcharacterofthem-reduction

proceduretoconstructappropriatetwistedCFTmodels,calledTwistedModels(TM),whichbyconstructionreproducetheQuantumHalltopologicalpropertiesatthose llings.IndeedfortheJainplateauxwe ndthatthedi erentdescriptionsgivenintheliteraturefallintodi erentsectorsoftheTMforthetorustopology.Otherinterestingaspectsareexplicitlyseenforthem=2nonstandard llingν=1

).FurthermorebyusingBoundaryCFTtechniquesthepresenceof

localizedimpuritiesand/ordissipationisshowntobecloselyconnectedwiththetwistedsectoroftheTM,whosepresenceassurestheconsistencyoftheconstructionandwhoseroleindescribingnontrivialglobalpropertiesof2Dquantumcondensedmattersystemsisstillunderstudy.2

Keywords:Vertexoperator,ConformalFieldTheory,QuantumHallE ect