A Unifying Conformal Field Theory Approach to the Quantum Hall Effect

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

RecentResearchDevelopmentsinPhysics

arXiv:hep-th/0507111v1 12 Jul 2005AUNIFYINGCONFORMALFIELDTHEORYAPPROACHTOTHEQUANTUMHALLEFFECTGerardoCristofanoDipartimentodiScienzeFisiche,Universit´adiNapoli“FedericoII”INFN,SezionediNapoli-ViaCintia-Compl.universitarioM.Sant’Angelo-80126Napoli,ItalyGiuseppeMaiellaDipartimentodiScienzeFisiche,Universit´adiNapoli“FedericoII”INFN,SezionediNapoli-ViaCintia-Compl.universitarioM.Sant’Angelo-80126Napoli,ItalyVincenzoMarottaDipartimentodiScienzeFisiche,Universit´adiNapoli“FedericoII”INFN,SezionediNapoli-ViaCintia-Compl.universitarioM.Sant’Angelo-80126Napoli,ItalyAdeleNaddeo

DipartimentodiScienzeFisiche,Universit´adiNapoli“FedericoII”

andCoherentia-INFM,Unit`adiNapoli-ViaCintia-Compl.universitarioM.Sant’Angelo-80126Napoli,ItalyGiulianoNiccoli

SissaandINFN,SezionediTrieste-ViaBeirut1-34100Trieste,Italy

RUNNINGTITLE:AUNIFYINGCFTFORTHEQUANTUMHALLEFFECT

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

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

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