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　　Recentyearshavebroughtarevivalofworkonstringtheory,whichhasbeenasourceoffascinationsinceitsoriginsnearlytwentyyearsago.Thereseemstobeawidelyperceivedneedforasystematic,pedagogicalexpositionofthepresentstateofknowledgeaboutstringtheory.Wehopethatthisbookwillhelptomeetthisneed.Togiveacomprehensiveaccountofsuchavasttopicasstringtheorywouldscarcelybepossible,evenintwovolumeswiththelengthtowhichthesehavegrown.Indeed,wehavehadtoomitmanyimportantsubjects,whiletreatingothersonlysketchily.Stringfieldtheoryisomittedentirely(thoughthesubjectofchapter11iscloselyrelatedtolight-conestringfieldtheory).Conformalfieldtheoryisnotdevelopedsystematically,thoughmuchofthebackgroundmaterialneededtounderstandrecentpapersonthissubjectispresentedinchapter3andelsewhere.

Preface

1Introduction

1.1Theearlydaysofdualmodels

1.1.1TheVenezianoamplitudeandduality

1.1.2High-energybehavioroftheVenezianomodel

1.1.3RamificationsoftheVenezianomodel

1.2Dualmodelsofeverything

1.2.1Dualityandthegraviton

1.2.2Unificationinhigherdimensions

1.2.3Supersymmetry

1.3Stringtheory

1.3.1Themasslesspointparticle

1.3.2Generalizationtostrings

1.3.3Constraintequations

1.4Stringinteractions

4.1Splittingofstrings

1.4.2Vertexoperators

1.4.3Useofvertexoperators

1.4.4Evaluationofthescatteringamplitude

1.4.5Themassofthegraviton

1.5Otheraspectsofstringtheory

1.5.1GravitationalWardidentities

1.5.2Openstrings

1.5.3Internalsymmetriesofopenstrings

1.5.4RecoveryoftheVenezianoamplitude

1.5.5ComparisonwithQCD

1.5.6Upitarityandgravity

1.6Conclusion

2Freebosonicstrings

2.1Theclassicalbosonicstring

2.1.1Stringactionanditssymmetries

2.1.2ThefreestringinMinkowskispace

2.1.3Classicalcovariantgaugefixingandfieldequations

2.2Quantization-oldcovariantapproach

2.2.1Commutationrelationsandmodeexpansions

2.2.2Virasoroalgebraandphysicalstates

2.2.3Vertexoperators

2.3Light-conegaugequantization

2.3.1Light-conegaugeandLorentzalgebra

2.3.2Constructionoftransversephysicalstates

2.3.3Theno-ghosttheoremandthespectrum-generatingalgebra

2.3.4Analysisofthespectrum

2.3.5Asymptoticformulasforleveldensities

2.4Summary

3Moderncovariantquantization

3.1Covariantpath-integralquantization

3.1.1Fazideev-P0povghosts

3.1.2Complexworld-sheettensorcalculus

3.1.3Quantizatlonoftheghosts3.2.1ConstructionofBRSTcharge

3.2.2CovariantcalculationoftheVirasoroanomaly

3.2.3Virasoro，conformalandgravitationalanomalies

3.2.4Bosonizationofghostcoordinates

3.3Globalaspectsofthestringworldsheet

3.4Stringsinbackgroundfields

3.4.1Introductionofabackgroundspa~~e-timemetric

3.4.2Weylinvariance

3.4.3Conformalinvarianceandtheequationsofmotion

3.4.4String-theoreticcorrectionstogeneralrelativity

3.4.5Inclusionofothermodes

3.4.6Thedilatonexpectationvalueandthestringcouplingconstant

3.5Summary

4World-sheetsupersymmetryinstringtheory

4.1Theclassicaltheory

4.1.1Globalworld-sheetsupersymmetry

4.1.2Superspace

4.1.3Constraintequations

4.1.4Boundaryconditionsandmodeexpansions

4.2Quantization-theoldcovariantapproach

4.2.1Commutationrelationsandmodeexpansions

4.2.2Super-Virasoroalgebraandphysicalstates

4.2.3Boson-emissionvertexoperators

4.3Light-conegaugequantization

4.3.1Thelight-conegauge

4.3.2No-ghosttheoremandthespectrum-generatingalgebra

4.3.3TheGSOconditions

4.3.4Locallysupersymmetricformoftheaction

4.3.5Superstringactionanditssymmetries

4.4Moderncovariantquantization

4.4.1Faddeev-Popovghosts

4.4.2BRSTsymmetry

4.4.3CovariantcomputationoftheVirasoroanomaly

4.5Extendedworld-sheetsupersymmetry

4.5.1TheN=2theory

4.5.2TheN=4theory

4.6Summary

4.ASuperYang-Millstheories

5Space-timesupersymmetryinstringtheory

5.1Theclassicaltheory

5.1.1Thesuperparticle

5.1.2Thesupersymmetricstringaction

5.1.3Thelocalfermionicsymmetry

5.1.4TypeIandtypeIIsuperstrings

5.2Quantization

5.2.1Light-conegauge

5.2.2Super-Poincar

5.3.2Closedsuperstrings

5.4Remarksconcerningcovariantquantization

5.5Summary

5.APropertiesofSO(2n)groups

5.BThespin(8)Cliffordalgebra

6Nonabeliangaugesymmetry

6.1Openstrings

6.1.1TheChan-Patonmethod

6.1.2Allowedgaugegroupsand：representations

6.2Currentalgebraonthestringworldsheet

6.3Heteroticstrings

6.3.1TheSO(32)theory

6.3.2TheEsxEstheory

6.4Toroidalcompactification

6.4.1Compactificationonacircle

6.4.2Fermionization

6.4.3Bosonizeddescriptionoftheheteroticstring

6.4.4Vertexoperatorrepresentations

6.4.5Formulasforthecocycles

6.4.6ThefullcurrentMgebra

6.4.7TheEsandspin(32)/Z2lattices

6.4.8Theheteroticstringspectrum

6.5Summary

6.AElementsofEs

6.BModularforms

7Treeamplitudes

7.1Bosonicopenstrings

7.1.1Thestructureoftreeamplitudes

7.1.2Decouplingofghosts

7.1.3Cyclicsymmetry

7.1.4Examples

7.1.5Tree-levelgaugeinvariance

7.1.6Thetwistoperator

7.2Bosonicclosedstrings

7.2.1Constructionoftreeamplitudes

7.2.2Examples

7.2.3Relationshiptoopen-stringtrees

7.3SuperstringsintheRNSformulation

7.3.1Open-stringtreeamplitudesinthebosonicsector

7.3.2TheF1picture

7.3.3Examples

7.3.4Treeamplitudeswithonefermionline

7.3.5Fermion-emissionvertices

7.4Superstringsinthesupersymmetricformulation

7.4.1Masslessparticlevertices

7.4.2Open-stringtrees

7.4.3Closed-stringtrees

7.4.4Heterotic-stringtrees

7.5Summary

7.ACoherent-statemethodsandcorrelationfunctions

Bibliography

Index

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