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Demystified SeriesAccounting DemystifiedAdvanced Calculus DemystifiedAdvanced Physics DemystifiedAdvanced Statistics DemystifiedAlgebra DemystifiedAlternative Energy DemystifiedAnatomy DemystifiedAstronomy DemystifiedAudio DemystifiedBiochemistry DemystifiedBiology DemystifiedBiotechnology DemystifiedBusiness Calculus DemystifiedBusiness Math DemystifiedBusiness Statistics DemystifiedC DemystifiedCalculus DemystifiedChemistry DemystifiedCircuit Analysis DemystifiedCollege Algebra DemystifiedComplex Variables DemystifiedCorporate Finance DemystifiedDatabases DemystifiedDiabetes DemystifiedDifferential Equations DemystifiedDigital Electronics DemystifiedDiscrete Mathematics DemystifiedEarth Science DemystifiedElectricity DemystifiedElectronics DemystifiedEngineering Statistics DemystifiedEnvironmental Science DemystifiedEveryday Math DemystifiedFertility DemystifiedFinancial Planning DemystifiedForensics DemystifiedFrench DemystifiedGenetics DemystifiedGeometry DemystifiedGerman DemystifiedGlobal Warming and Climate Change DemystifiedHedge Funds DemystifiedInvesting DemystifiedItalian DemystifiedJava DemystifiedJavaScript DemystifiedLean Six Sigma DemystifiedLinear Algebra DemystifiedMacroeconomics DemystifiedManagement Accounting DemystifiedMath Proofs DemystifiedMath Word Problems DemystifiedMATLAB DemystifiedMedical Billing and Coding DemystifiedMedical Charting DemystifiedMedical-Surgical Nursing DemystifiedMedical Terminology DemystifiedMeteorology DemystifiedMicrobiology DemystifiedMicroeconomics DemystifiedNanotechnology DemystifiedNurse Management DemystifiedOOP DemystifiedOptions DemystifiedOrganic Chemistry DemystifiedPharmacology DemystifiedPhysics DemystifiedPhysiology DemystifiedPre-Algebra DemystifiedPrecalculus DemystifiedProbability DemystifiedProject Management DemystifiedPsychology DemystifiedQuantum Field Theory DemystifiedQuantum Mechanics DemystifiedReal Estate Math DemystifiedRelativity DemystifiedRobotics DemystifiedSales Management DemystifiedSignals and Systems DemystifiedSix Sigma DemystifiedSpanish DemystifiedSQL DemystifiedStatics and Dynamics DemystifiedStatistics DemystifiedString Theory DemystifiedTechnical Analysis DemystifiedTechnical Math DemystifiedTrigonometry DemystifiedVitamins and Minerals Demystified
String TheoryDemystifiedDavid McMahonNew York Chicago San Francisco Lisbon LondonMadrid Mexico City Milan New Delhi San JuanSeoul Singapore Sydney Toronto
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For more information about this title, click hereCONTENTSPrefacexiCHAPTER 1IntroductionA Quick Overview of General RelativityA Quick Primer on Quantum TheoryThe Standard ModelQuantizing the Gravitational FieldSome Basic Analysis in String TheoryUnification and Fundamental ConstantsString Theory OverviewSummaryQuiz123881011121818CHAPTER 2The Classical String I: Equations of MotionThe Relativistic Point ParticleStrings in Space-TimeEquations of Motion for the StringThe Polyakov ActionMathematical Aside: The Euler CharacteristicLight-Cone CoordinatesSolutions of the Wave EquationOpen Strings with Free EndpointsClosed Strings21222832363639434446
viString Theory DemystifiedOpen Strings with Fixed EndpointsPoisson BracketsQuiz474949The Classical String II: Symmetries andWorldsheet CurrentsThe Energy-Momentum TensorSymmetries of the Polyakov ActionTransforming to a Flat Worldsheet MetricConserved Currents from Poincaré InvarianceThe HamiltonianSummaryQuiz5152535963676767CHAPTER 4String QuantizationCovariant QuantizationLight-Cone QuantizationSummaryQuiz6970858787CHAPTER 5Conformal Field Theory Part IThe Role of Conformal Field Theoryin String TheoryWick RotationsComplex CoordinatesGenerators of Conformal TransformationsThe Two-Dimensional Conformal GroupCentral ExtensionClosed String Conformal Field TheoryWick ExpansionOperator Product 4BRST QuantizationBRST Operators and Introductory RemarksBRST-Invariant States115116118CHAPTER 3CHAPTER 6
viiContentsBRST in String Theory-CFTBRST TransformationsNo-Ghost TheoremSummaryQuiz120121125125126CHAPTER 7RNS SuperstringsThe Superstring ActionConserved CurrentsThe Energy-Momentum TensorMode Expansions and Boundary ConditionsSuper-Virasoro GeneratorsCanonical QuantizationThe Super-Virasoro AlgebraThe Open String SpectrumGSO ProjectionCritical 149150150CHAPTER 8Compactification and T-DualityCompactification of the 25th DimensionModified Mass SpectrumT-Duality for Closed StringsOpen Strings and 65CHAPTER 9Superstring Theory ContinuedSuperspace and SuperfieldsSuperfield for Worldsheet SupersymmetryGrassman IntegrationA Manifestly Supersymmetric ActionThe Green-Schwarz ActionSpace-Time Supersymmetry and Strings167168171173174175180
viiiString Theory DemystifiedLight-Cone GaugeCanonical QuantizationSummaryQuiz181184185186CHAPTER 10A Summary of Superstring TheoryA Summary of Superstring TheorySuperstring TheoryDualitiesQuiz187187190192193CHAPTER 11Type II String TheoriesThe R and NS SectorsThe Spin FieldType II A String TheoryType II B TheoryThe Massless Spectrum of Different SectorsSummaryQuiz195195200201203203204205CHAPTER 12Heterotic String TheoryThe Action for SO(32) TheoryQuantization of SO(32) TheoryThe SpectrumCompactification and Quantized MomentumSummaryQuiz207208209214216219219CHAPTER 13D-BranesThe Space-Time ArenaQuantizationD-Branes in Superstring TheoryMultiple D-BranesTachyons and D-Brane DecaySummaryQuiz221223225230230235237237
ContentsCHAPTER 14CHAPTER 15CHAPTER 16ixBlack HolesBlack Holes in General RelativityCharged Black HolesThe Laws of Black Hole MechanicsComputing the Temperature of a Black HoleEntropy Calculations for Black Holeswith String TheorySummaryQuizThe Holographic Principle and AdS/CFTCorrespondenceA Statement of the Holographic PrincipleA Qualitative Description of AdS/CFTCorrespondenceThe Holographic Principle and M-TheoryMore 55256257258260262262String Theory and CosmologyEinstein’s EquationsInflationThe Kasner MetricThe Randall-Sundrum ModelBrane Worlds and the Ekpyrotic UniverseSummaryQuiz265266266268273275277278Final Exam279Quiz Solutions285Final Exam Solutions291References297Index299
ABOUT THE AUTHORDavid McMahon has worked for several years as a physicist and researcher atSandia National Laboratories. He is the author of Linear Algebra Demystified,Quantum Mechanics Demystified, Relativity Demystified, MATLAB Demystified, andComplex Variables Demystified, among other successful titles.Copyright 2009 by The McGraw-Hill Companies, Inc. Click here for terms of use.
PREFACEString theory is the greatest scientific quest of all time. Its goal is nothing other thana complete description of physical reality—at least at the level of fundamentalparticles, interactions, and perhaps space-time itself. In principle, once thefundamental theory is fully known, one could derive relativity and quantum theoryas low-energy limits to strings. The theory sets out to do what no other has beenable to since the early twentieth century—combine general relativity and quantumtheory into a single unified framework. This is an ambitious program that hasoccupied the best minds in mathematics and physics for decades. Einstein himselffailed, but he lacked key ingredients that are necessary to pull it off.String theory comes attached with a bit of controversy. As anyone who is readingthis book likely knows, experimentally testing it is not an immediately accessibleoption due to the high energies required. It is, after all, a theory of creation itself—so the energies associated with string theory are of course very large. Nonetheless,it now appears that some indirect tests are possible and the timing of this book maycoincide with some of this program. The first clue will be the continued search forsupersymmetry, the theory that proposes fermions and bosons have superpartners,that is, a fermion like an electron has a sister superpartner particle that is a boson.Superparticles have not been discovered, so if it exists supersymmetry must bebroken somehow so that the super partners have high mass. This could explain whywe haven’t seen them so far. But the Large Hadron Collider being constructed inEurope as we speak may be able to discover evidence of supersymmetry. This doesnot prove string theory, because you can have supersymmetry work just fine withpoint particles. However, supersymmetry is absolutely essential for string theory towork. If supersymmetry does not exist, string theory cannot be true. If supersymmetryis found, while it does not prove string theory, it is a good indication that stringtheory might be right.Recent theoretical work also opens up the intriguing possibility that there mightbe large extra dimensions and that they might be inferred in experimental tests.Only gravity can travel into the extra space scientists call the “bulk.” At the energiesof the Large Hadron Collider, it might be possible to see some evidence that this isCopyright 2009 by The McGraw-Hill Companies, Inc. Click here for terms of use.
xiiString Theory Demystifiedhappening, and some have even proposed that microscopic black holes could beproduced. Again, you could imagine having extra dimensions without string theory,so discoveries like these would not prove string theory. However, they would bemajor indirect evidence in its favor. You will learn in this book that string theorypredicts the existence of extra dimensions, so any evidence of this has to be takenas a serious indication that string theory is on the right path.String theory has lots of problems—it’s a work in progress. This time is akin toliving in the era when the existence of atoms was postulated but unproven andskeptics abounded. There are lots of skeptics out there. And string theory does seema bit crazy—there are several versions of the theory, and each has a myriad ofparticle states that have not been discovered (however, note that transformationscalled dualities have been discovered that relate the different string theories, andwork is underway on an underlying theory believed to exist called M-theory). Theonly serious competitor right now for string theory is loop quantum gravity. I wantto emphasize I am not an expert, but I once took a seminar on it and to be honest Ifound it incredibly distasteful. It seemed so abstract it almost didn’t seem likephysics at all. It struck me more as mathematical philosophy. String theory seems alot more physical to me. It makes outlandish predictions like the existen
Precalculus Demystified Probability Demystified Project Management Demystified Psychology Demystified Quantum Field Theory Demystified Quantum Mechanics Demystified Real Estate Math Demystified Relativity Demystified Robotics Demystified Sales Management Demystified Signals and Systems Demystified Six Sigma Demystified Spanish Demystified SQL Demystified Statics and
