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1、MITOpenCourseWarehttp://ocw.mit.edu8.821StringTheoryFall2008ForinformationaboutcitingthesematerialsorourTermsofUse,visit:http://ocw.mit.edu/terms.8.821F2008Lecture03:Thedecouplingargument;AdS/CFTwithoutstringtheory,adiscoverywithhindsightLecturer:McGreevy
2、September14,2008Today:1.Backreactionanddecoupling2.Aboldassertion3.Hints,lore,prophesyRecallfromlasttimethat:•D-branesaresubspaceswhereopenstringscanend.Nomenclature:Dp-braneshavepspatialdimensions.•Lightopenstringsarelocalizedatthebrane,andrepresenttheflu
3、ctuationsofthebrane.•D-branescarryRRcharges(whichsaturateDiracquantizationcondition;thisisnecessarysincewehavebothelectricandmagneticcharges).ThiscanbeseenbycomputingtheamplitudeforD-branestoemitRRgaugebosons;itisdescribedbyworldsheetsasinthefigurebelow.•T
4、heworldvolumetheoryonthebraneisaYMtheory.DpFigure1:ThediskamplitudefortheemissionofaclosedstringbyaD-brane.ThediskamplitudefortheemissionofagravitongivesthetensionoftheD-braneandisproportionalto−2+2h+b1gs=.(1)gs1ThebackreactiononthegeometryfromNcoincident
5、D-branesisdeterminedfromEinsteinequations1brane21Rµν−Rgµν=8πGNTµν∝gs··N=gsN=λ,(2)2gswhereweusedthefactthatG∝closedstringcoupling∝g2.(3)NsAtsmallλ,thebackreactionisnegligibleandthephysicsisdecribedbyclosedstringseverywhere(theseareexcitationsofemptyspace)p
6、lusopenstrings(YM+α′F4+···)localizedonthebranes(theseareexcitationsofthebranes)inflatspace.Atlargeλ,theD-braneswillgravitationallycollapseintoanRRsoliton(blackholewiththesamecharge).Forp>0,theblackholeisnotapointparticle,butisalsoextendedinpspatialdimensio
7、ns.Thecaseofp=3The3-branewillfill3+1dimensions(e.g.,xµ=0,1,2,3).Wecanputthebraneaty1=···=y6=0,�i.e,theR3,1isatapointinthetransverseR6.Letr2=yi2bethedistancefromthebrane,thenthemetricofthebranewilltaketheformR6����R3,11������6ds2=�ηdxµdxν+H(r)dy2,(4)µνiH(r)
8、i=1andL2H(r)=1+,dy2=dr2+r2dΩ,(5)r45whereH(r)→1forlargerandLislikeanADMmass.TheRRF5satisfies�F5=N.(6)S5atconstantrThesolutionlookslikeanRNblackhole(Figure2).Faraway(largerwithH(r)=1),thesolutionwillasymptotetoR9,1.Nea
