introduction to supersymmetry

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1、IntroductiontoSupersymmetryAdelBilalInstituteofPhysics,UniversityofNeuch^atelrueBreguet1,2000Neuch^atel,Switzerlandadel.bilal@unine.chAbstractarXiv:hep-th/0101055v110Jan2001TheseareexpandednotesoflecturesgivenatthesummerschoolGif2000"inParis.TheyconstitutetherstpartofanIntroductiont

2、osupersymmetryandsupergravity"withthesecondpartonsupergravitybyJ.-P.Derendingertoappearsoon.Thepresentintroductioniselementaryandpragmatic.Idiscuss:spinorsandthePoincaregroup,thesusyalgebraandsusymultiplets,supereldsandsusylagrangians,susygaugetheories,spontaneouslybrokensusy,thenon-

3、linearsigmamodel,N=2susygaugetheories,andnallySeiberg-Wittenduality.iiiiContents1Introduction12SpinorsandthePoincaregroup32.1TheLorentzandPoincaregroups..................32.2Spinors.................................43Thesusyalgebraanditsrepresentations93.1Thesupersymmetryalgebra.....

4、................93.2Somebasicproperties.........................103.3Masslesssupermultiplets.......................113.4Massivesupermultiplets.......................134Superspaceandsuperelds174.1Superspace...............................174.2Chiralsuperelds...........................2

5、04.3Susyinvariantactions........................214.4Vectorsuperelds...........................235Supersymmetricgaugetheories275.1PureN=1gaugetheory.......................275.2N=1gaugetheorywithmatter...................30iiiivCONTENTS5.3SupersymmetricQCD........................326Spon

6、taneouslybrokensupersymmetry356.1Vacuainsusytheories........................356.2TheGoldstonetheoremforsusy...................376.3Mechanismsforsusybreaking....................386.3.1O'Raifeartaighmechanism..................386.3.2Fayet-Iliopoulosmechanism.................396.4Massform

7、ula.............................397Thenon-linearsigmamodel437.1Chiralmultipletsonly........................437.2Includinggaugeelds.........................478N=2susygaugetheory518.1N=2superYang-Mills.......................518.2EectiveN=2gaugetheories....................539Seiberg-W