We calculate the NS-R fermionic zero-norm states of type II string spectrum. The massless and some possible massive zero-norm states are identified to be responsible for the space-time supersymmetry. The existence of other fermionic massive zero-norm state

I.INTRODUCTION

Ithasbeenknownforawhilethatthecompletespace-timesymmetryofstringtheoryiscloselyrelatedtotheexistenceofzero-normstates[1]intheoldcovariantquantizationofthestringspectrum.[2]Thisincludethew∞symmetryof2dLiouvilletheoryandthediscreteT-dualitysymmetryofclosedbosonicstring.[3]However,allpreviousstudywasaboutthebosonicsectorandnothinghasbeensaidaboutthesymmetriesofNS-R(NevenuSchwars-Ramond)andR-Rsectors,ex.NS-Rsupersymmetryzero-normstates.Ontheotherhand,recentstudyhasrevealedthatD-braneisthesymmetrychargecarrierofmasslessR-Rstate.

[4]Afurtherstudyfromzero-normstatepointofviewmayholdthekeytouncoverthewholesetofR-Rchargesincludingthemassiveones.

Inthispaper,wewillidentifythefermioniczero-normstateswhichareresponsibleforthespace-timesupersymmetryintheNS-RsectorofTypeIIstring.Thisincludesthemasslessandsomepossiblemassiveonessincesupersymmetryisanexactsymmetryateach xedmasslevelofthespectrum.Forsimplicity,wewillcalculatethezero-normstatesuptothe rstmassivelevel.Inadditiontothesupersymmetryzero-normstates,wediscoverothermassivezero-normstateswithhigherspinor-tensorindiceswhich,presumably,correspondtonewenlargedmassiveboson-fermionsymmetriesofthetheory.WethencalculatethemasslessR-Rzero-normstates.Itisfoundthattheyhaveexactlythesamedegreeoffreedomwiththoseofthepositive-normphysicalpropagatingR-Rgauge elds,andthusdonot tintotheR-Rchargedegreeoffreedom.WeconcludethatthemasslessR-Rzero-normstatesdonotcorrespondtothechargesofmasslessR-Rgauge elds.ThereisnoperturbativestringstateswhichcarriesthemasslessR-Rcharges.Thisisverydi erentfromtheNS-NSandNS-Rsectors.AfurtherstudyofthemeaningofthesemasslessR-Rzero-normstatesseemsnecessary.Ontheotherhand,theexistenceofmassiveR-Rzero-normstatesmayimplythatsomemassiveperturbativestringR-RstatesdocarrysomekindsofmassiveR-Rcharges.Weproposeamethodtojustifythisimportantissue.

Thispaperisorganizedasfollowing.InsectionII,wecalculatetheNSzero-normstates