lecture05 how to defend yourself from a supersymmetric field theory

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1、MITOpenCourseWarehttp://ocw.mit.edu8.821StringTheoryFall2008ForinformationaboutcitingthesematerialsorourTermsofUse,visit:http://ocw.mit.edu/terms.8.821F2008Lecture5:SUSYSelf-DefenseLecturer:McGreevySeptember22,2008Today’slecturewillteachyouenoughsupersymmetrytodefendyourselfagainstah

2、ostilesuper-symmetricfieldtheory,shouldyoumeetonedownadarkalleyway.Topicswillinclude1.SUSYrepresentationtheory,includingbasicideasregardingthealgebraandanexplanationofwhyN=4ismaximal(aproofduetoNahm)2.PropertiesofN=4SuperYang-Millstheory,suchasthespectrumandwhereitcomesfrominstringthe

3、ory.Beforeplungingin,wemightbeinclinedtowonder:whyissupersymmetrysowonderful?Inadditiontothedelightfulpropertiesthatwillbeexploredintheremainderofthiscourse,therearevariousreasonsarisingfrompureparticlephysics:forexample,itstabilizestheelectroweakhierarchy,changesthetrajectoryofRGflow

4、ssuchthatthegaugecouplingsunifyatveryhighenergies,andhalvestheexponentinthecosmologicalconstantproblem.Theseareissuesthatwewillnotexplorefurtherinthislecture.1SUSYRepresentationTheoryind=4Webeginwithaquickreviewofold-fashionedPoincaresymmetryind=4:1.1PoincaregroupRecallthattheisometr

5、ygroupofMinkowskispaceisthePoincaregroup,consistingoftranslations,rotations,andboosts.ThevariouschargesassociatedwiththesubgroupsofthePoincaregrouparequitefamiliarandarelistedbelowChargeSubgroupTranslationsPµR3,1Rotations/boostsMµνSO(3,1)∼(SU(2)×SU(2))1Luckilytherotation/boostpartoft

6、healgebraSO(3,1)decomposes(atleastinthesenseofthe“sloppyrepresentationtheory”thatwearedoingtoday)intotwocopiesofSU(2).WeareallfamiliarwithrepresentationsofSU(2),eachofwhicharelabeledbyahalf-integersi∈0,1/2,1,...;theproductoftwooftheserepsgivesusarepofSO(3,1):(s1,s2)Scalar(0,0)4-vecto

7、r(1/2,1/2)Symmetrictensor(1,1)Weylfermions(1/2,0),(0,1/2)Self-dual,anti-self-dualtensors(1,0),(0,1)Havingmasteredthisgroup,wewonderwhetherwecouldpossiblyhavealargerspacetimesymmetrygrouptodealwith,leadingustotheideaofenlargingthePoincaregroupbyaddingfermionicgenerators!1.2Supercharge

8、sLet’scallth