phong_lectures on supersymmetric yang-mills theory and integrable systems

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1、UCLA/99/TEP/28Columbia/Math/99LecturesonSupersymmetricYang-MillsTheoryandIntegrableSystemsEricD’HokeraandD.H.PhongbaDepartmentofPhysicsUniversityofCalifornia,LosAngeles,CA90095bDepartmentofMathematicsColumbiaUniversity,NewYork,NY10027AbstractWepresentaseriesoffourself-containedlectureson

2、thefollowingtopics;(I)Anintroductionto4-dimensional1≤N≤4supersymmetricYang-Millstheory,includingparticleandfieldcontents,N=1andN=2superfieldmethodsandtheconstructionofgeneralinvariantLagrangians;(II)AreviewofholomorphicityanddualityinN=2super-Yang-Mills,ofSeiberg-Wittentheoryanditsformulat

3、ionintermsofRiemannsurfaces;(III)AnintroductiontomechanicalHamiltonianintegrablesystems,suchasthearXiv:hep-th/9912271v129Dec1999TodaandCalogero-MosersystemsassociatedwithgeneralLiealgebras;areviewoftherecentlyconstructedLaxpairswithspectralparameterfortwistedanduntwistedellipticCalogero-

4、Mosersystems;(IV)AreviewofrecentsolutionsoftheSeiberg-WittentheoryforgeneralgaugealgebraandadjointhypermultipletcontentintermsoftheellipticCalogero-Moserintegrablesystems.Contents1Introduction41.1SupersymmetryandtheStandardModel...................41.2SupersymmetryandUnificationofForces...

5、................61.3SupersymmetricYang-Millsdynamics.....................92SupersymmetricYang-Millsin4Dimensions102.1SupersymmetryAlgebra............................102.2MasslessParticleRepresentations.......................112.3MassiveParticleRepresentations.......................122.4F

6、ieldContentsofSupersymmetricFieldTheories..............132.5N=1SupersymmetricLagrangians.......................142.6N=1SuperfieldMethods............................152.7IrreducibleSuperfieldsofN=1.........................172.8GeneralN=1SusyLagrangiansviaSuperfields................202.9Renor

7、malizableN=2,4SusyLagrangians...................222.10N=2SuperfieldMethods:unconstrainedsuperspace............232.11N=2SuperfieldMethods:harmonic/analyticsuperspaces..........263Seiberg-WittenTheory303.1WilsonEffectiveCouplingsandActions....................303.2Holomorphicit