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1、CERN-TH/2002-025ROM2F-2002/08LPTENS02/14CPHTRR020.0202hep-th/0204089OpenStringsCAngelantonjyandASagnottizyTheoryDivision{CERN,1211Geneva23,SwitzerlandzDipartimentodiFisica,UniversitadiRomaTorVergata",INFN-SezionediRomaTorVergata",ViadellaRicercaScienti ca1,I-00133RomaAbst
2、ract.Thisreviewisdevotedtoopenstrings,andinparticulartotheoftensurprisingfeaturesoftheirspectra.ItfollowsandsummarizesdevelopmentsthattookplacemainlyattheUniversityofRomeTorVergata"overthelastdecade,andcentredonworld-sheetaspectsoftheconstructionsnowcommonlyreferredtoasori
3、entifolds".Ourpresentationaimstobridgethegapbetweentheworld-sheetanalysis,that rstexhibitedmanyofthenovelfeaturesofthesesystems,andtheirgeometricdescriptionintermsofextendedobjects,D-branesandO-planes,contributedbymanyothercolleagues,andmostnotablybyJ.Polchinski.Wethereforep
4、roceedthroughanumberofprototypeexamples,startingfromthebosonicstringandmovingontoten-dimensionalfermionicstringsandtheirtoroidalandorbifoldcompacti cations,inanattempttoguidethereaderinaself-containedjourneytothemorerecentdevelopmentsrelatedtothebreakingofsupersymmetry.PACSn
5、umbers:11.25.w,11.25.Db,11.25.Hf,11.25.MjarXiv:hep-th/0204089v110Apr2002DedicatedtoJohnH.SchwarzontheoccasionofhissixtiethbirthdayContents2Contents1Introductionandsummary32Thebosonicstring62.1ThePolyakovexpansion...........................62.2Light-conequantization..........
6、..................132.3Chan-Patongroupsandquarks"attheendsofstrings..........172.4VacuumamplitudeswithzeroEulercharacter...............213Ten-dimensionalsuperstrings303.1SuperstringsintheNSRformulation....................313.2ThetypeIsuperstring:SO(32)vsUSp(32).............
7、....373.3Opendescendantsofthe0Amodel.....................403.4Opendescendantsofthe0Bmodel.....................414Toroidalcompacti cation464.1Theone-dimensionaltorus..........................464.2Higher-dimensionaltori............................524.3T-dualityanddiscretemodul
8、i........................565Orbifoldcompacti cation595.1Theone-dimensionalo
