A Unifying Conformal Field Theory Approach to the Quantum Ha(4)

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

[23]G.Cristofano,V.Marotta,G.Niccoli,JHEP0406(2004)056.

[24]V.Kac,A.Radul,Comm.Math.Phys.157(1993)429;E.Frenkel,V.Kac,A.Radul,W.

Wang,Comm.Math.Phys.170(1995)337;H.Awata,M.Fukuma,Y.Matsuo,S.Odake,Prog.Theor.Phys.(Supp.)118(1995)343.

[25]F.D.M.HaldaneandE.H.Rezayi,Phys.Rev.Lett.60956(1988);Phys.Rev.Lett.601886

(1988).

[26]J.D.Naud,L.P.Pryadko,S.L.Sondhi,Nucl.Phys.B565(2000)572.

[27]A.Cappelli,G.R.Zemba,Nucl.Phys.B490(1997)595.

[28]A.Cappelli,L.S.GeorgievandI.T.Todorov,Commun.Math.Phys.205657(1999)

[29]K.Ino,Nucl.Phys.532B(1998)783.

[30]P.DiFrancesco,P.MathieuandD.Senechal,

(1996).ConformalFieldTheories,Springer-Verlag,

[31]D.C.Cabra,A.LopezandG.L.RossiniEur.Phys.J.19B(2001)21.

[32]T.L.Ho,Phys.Rev.Lett.75(1995)1186.

[33]C.Nayak,F.Wilczek,Nucl.Phys.B479(1996)529.

[34]M.OshikawaandI.A eck,Nucl.Phys.B495(1997)533.

[35]N.Ishibashi,Phys.Lett.A4(1989)251;J.L.Cardy,Nucl.Phys.B324(1989)581.

[36]V.B.PetkovaandJ.B.Zuber,Phys.Lett.B504,(2001)157;U.Grimm,“Dualityandconformal

twistedboundariesintheIsingmodel”,hep-th/0209048.

[37]A.Cappelli,G.D’Appollonio,JHEP02(2002)039;J.Fuchs,C.Schweigert,Phys.Lett.B414

(1997)251.

[38]I.A eck,A.W.W.Ludwig,Phys.Rev.Lett.67(1991)161;I.A eck,A.W.W.Ludwig,Phys.

Rev.B48(1993)7297.

[39]C.Nayak,M.P.A.Fisher,A.W.W.Ludwig,H.H.Lin,Phys.Rev.B59(1999)15694;H.Yi,C.

L.Kane,Phys.Rev.B57(1998)R5579.

[40]P.Nozi`eres,A.Blandin,J.Phys.(Paris)41(1980)193;C.L.Kane,M.P.A.Fisher,Phys.Rev.

B46(1992)15233.

[41]G.Cristofano,D.Giuliano,G.Maiella,L.Valente,Int.Jou.Mod.Phys.B9(1995)707;Int.

Jou.Mod.Phys.B9(1995)3229;G.Cristofano,D.Giuliano,G.Maiella,Jou.dePhys.I(1996)861.

[42]C.G.Callan,I.R.Klebanov,J.M.Maldacena,A.Yegulalp,Nucl.Phys.B443(1995)444.

[43]L.Cappiello,G.Cristofano,G.Maiella,V.Marotta,Mod.Phys.Lett.A17(2002)1281.

[44]G.Cristofano,V.Marotta,G.Niccoli,hep-th/0412085.