Note: Cover -- Half-title -- Title -- Copyright -- Dedication -- Contents -- Preface -- NOTATION AND CONVENTIONS -- 1 Introduction -- 1.1 Historical origins -- 1.2 General features -- Gravity -- Yang-Mills gauge theory -- Supersymmetry -- Extra dimensions of space -- The size of strings -- 1.3 Basic string theory -- World-volume actions and the critical dimension -- Closed strings and open strings -- Perturbation theory -- Superstrings -- 1.4 Modern developments in superstring theory -- T-duality -- S-duality -- D-branes -- What is M-theory? -- F-theory -- Flux compactifications -- Black-hole entropy -- AdS/CFT duality -- String and M-theory cosmology -- 2 The bosonic string -- 2.1 p-brane actions -- Relativistic point particle -- Generalization to the p-brane action -- 2.2 The string action -- The Nambu-Goto action -- The string sigma model action -- 2.3 String sigma-model action: the classical theory -- Symmetries -- Gauge fixing -- Equations of motion and boundary conditions -- Equations of motion -- Boundary conditions -- Solution to the equations of motion -- Closed-string mode expansion -- 2.4 Canonical quantization -- Open-string mode expansion -- Hamiltonian and energy{momentum tensor -- Noether currents -- Hamiltonian -- Energy momentum tensor -- Mass formula for the string -- The Virasoro algebra -- Classical theory -- Quantum theory -- Physical states -- Mass operator -- Level matching -- Virasoro generators and physical states -- Absence of negative-norm states -- Spurious states -- Determination of a -- Determination of the space-time dimension -- Critical bosonic theory -- 2.5 Light-cone gauge quantization -- Mass-shell condition -- Analysis of the spectrum -- The open string -- The number of states -- The closed string -- 3 Conformal field theory and string interactions -- 3.1 Conformal field theory -- The conformal group in D dimensions. , The conformal group in two dimensions -- Conformal fields and operator product expansions -- Kac-Moody algebras -- Coset-space theories -- Minimal models -- 3.2 BRST quantization -- 3.3 Background fields -- The role of the dilaton -- Effective potential and moduli fields -- 3.4 Vertex operators -- 3.5 The structure of string perturbation theory -- Partition functions and scattering amplitudes -- The moduli space of Riemann surfaces -- 3.6 The linear-dilaton vacuum and noncritical strings -- 3.7 Witten's open-string field theory -- 4 Strings with world-sheet supersymmetry -- 4.1 Ramond-Neveu-Schwarz strings -- 4.2 Global world-sheet supersymmetry -- Superspace -- 4.3 Constraint equations and conformal invariance -- 4.4 Boundary conditions and mode expansions -- Open strings -- Closed strings -- 4.5 Canonical quantization of the RNS string -- Super-Virasoro generators and physical states -- Absence of negative-norm states -- 4.6 Light-cone gauge quantization of the RNS string -- Analysis of the spectrum -- The Neveu-Schwarz sector -- The Ramond sector -- Zero-point energies -- The GSO projection -- The massless closed-string spectrum -- 4.7 SCFT and BRST -- Superconformal field theory -- BRST symmetry -- 5 Strings with space-time supersymmetry -- 5.1 The D0-brane action -- Kappa symmetry -- 5.2 The supersymmetric string action -- Kappa symmetry -- 5.3 Quantization of the GS action -- The light-cone gauge -- The light-cone gauge action -- Canonical quantization -- Open type I superstring -- Closed strings -- The free string spectrum -- Open type I superstrings -- Type II superstring theories -- 5.4 Gauge anomalies and their cancellation -- Chiral fields -- Differential forms and characteristic classes -- Characterization of anomalies -- Type IIB superstring theory -- Type I superstring theory -- The supergravity multiplet -- The case of E8 x E8. , 6 T-duality and D-branes -- 6.1 The bosonic string and Dp-branes -- T-duality and closed strings -- T-duality and the sigma model -- T-duality and open strings -- Boundary conditions -- D-branes -- Open-string tachyons -- Chan-Paton charges, Wilson lines and multiple branes -- The spectrum -- 6.2 D-branes in type II superstring theories -- Form fields and p-brane charges -- Maxwell theory -- Generalization to p-branes -- Stable D-branes in type II superstring theories -- Non-BPS D-branes -- Type II superstrings and T-duality -- Mapping of coupling constants -- K-theory -- Type II D-branes -- 6.3 Type I superstring theory -- Orientifold projection -- Anomalies -- Other type I D-branes -- The type I theory -- 6.4 T-duality in the presence of background fields -- NS-NS sector fields -- R-R sector fields -- 6.5 World-volume actions for D-branes -- Kappa symmetric D-brane actions -- Counting of degrees of freedom -- Born-Infeld action -- D-brane tensions -- Bosonic D-brane actions with background fields -- The abelian case -- The nonabelian case -- The Myers effect -- 7 The heterotic string -- 7.1 Nonabelian gauge symmetry in string theory -- D-branes and orientifold planes -- Isometries of the internal space -- Heterotic strings -- 7.2 Fermionic construction of the heterotic string -- The SO(32) heterotic string -- Right-movers -- Left-movers -- Massless spectrum -- A GSO-type projection -- The E8 x E8 heterotic string -- Boundary conditions for fermions -- The n = 16 case -- 7.3 Toroidal compactification -- The bosonic string -- Mode expansions -- Mode expansions with constant background fields -- The mass spectrum and level-matching condition -- The moduli space -- Enhanced gauge symmetry -- The self-dual radius -- One-loop modular invariance -- Modular invariance of… -- Even self-dual lattices -- A brief introduction to lattices. , Lattices and toroidal compactifications -- Type II superstrings -- 7.4 Bosonic construction of the heterotic string -- Toroidal compactification of the heterotic string -- Duality and the heterotic string -- Appendix: The Poisson resummation formula -- 8 M-theory and string duality -- Low-energy e ective actions -- BPS branes -- 8.1 Low-energy effective actions -- Renormalizability -- Eleven-dimensional supergravity -- Field content -- Action -- Supersymmetry transformations -- Supersymmetric solutions -- M-branes -- Type IIA supergravity -- Fermionic fields -- Bosonic fields -- Coupling constants -- Action -- Supersymmetry transformations -- Type IIB supergravity -- Field content -- The self-dual five-form -- An action -- Supersymmetry transformations -- Global SL(2R) symmetry -- Type I supergravity -- Field content -- Action -- Supersymmetry transformations -- Heterotic supergravity -- Action -- Supersymmetry transformations -- 8.2 S-duality -- A double expansion -- Type I superstring - SO(32) heterotic string duality -- Nonperturbative test -- The fundamental type I string -- Type IIB S-duality -- Symmetry under… -- (p,q) strings -- Other BPS states -- 8.3 M-theory -- Type IIA superstring theory at strong coupling -- The D6-brane -- M-branes -- The D6-brane -- E8 x E8 heterotic string theory at strong coupling -- 8.4 M-theory dualities -- An M-theory/type IIB superstring duality -- Matching BPS brane tensions in nine dimensions -- An M-theory/SO(32) superstring duality -- U-duality -- A nongeometric duality of M-theory -- 9 String geometry -- Kaluza{Klein compactification -- Brane-world scenario -- Motivation -- A first glance at Calabi-Yau manifolds -- Conifold transitions and supersymmetric cycles -- Mirror symmetry -- Exceptional-holonomy manifolds -- 9.1 Orbifolds -- Some simple examples -- Compact examples -- Noncompact examples. , The spectrum of states -- Orbifolds and supersymmetry breaking -- The orbifold… -- 9.2 Calabi-Yau manifolds: mathematical properties -- Definition of Calabi-Yau manifolds -- Hodge numbers of a Calabi-Yau n-fold -- Hodge diamond -- 9.3 Examples of Calabi-Yau manifolds -- Calabi-Yau one-folds -- Noncompact example:… -- Compact example: T2 -- Calabi{Yau two-folds -- Noncompact examples -- Compact examples: T4, K3 -- Orbifold limit of K3 -- Blowing up the singularities -- Hodge numbers of K3 -- Calabi-Yau n-folds -- Submanifolds of complex projective spaces -- 9.4 Calabi-Yau compactifications of the heterotic string -- Ansatz for the D = 10 space-time geometry -- Maximally symmetric solutions -- Conditions for unbroken supersymmetry -- Properties of the external space -- Properties of the internal manifold -- Holonomy and unbroken supersymmetry -- Internal Dirac matrices -- Kahler form and complex structure -- Holomorphic three-form -- 9.5 Deformations of Calabi-Yau manifolds -- Antisymmetric tensor-field deformations -- Metric deformations -- A simple example: the torus -- Deformations of Calabi-Yau three-folds -- 9.6 Special geometry -- The metric on moduli space -- The complex-structure moduli space -- The Kahler potential -- Special coordinates -- The Kahler transformations -- The Kahler-structure moduli space -- The Kahler potential -- The form of the prepotential -- 9.7 Type IIA and type IIB on Calabi-Yau three-folds -- Type IIA -- Type IIB -- 9.8 Nonperturbative effects in Calabi-Yau compactifications -- The conifold singularity -- Supersymmetric cycles -- Special Lagrangian submanifolds -- Black-hole mass formula -- Holomorphic cycles -- 9.9 Mirror symmetry -- The circle -- The torus -- T3 fibrations -- 9.10 Heterotic string theory on Calabi-Yau three-folds -- 9.11 K3 compactifications and more string dualities. , Compactification of M-theory on K3.

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