Cover -- Half-title -- Series-title -- Title -- Copyright -- Dedication -- Contents -- List of inserts -- Preface -- 1 Overview and overture -- 1.1 The classical dynamics of geometry -- 1.2 Gravitons and photons -- 1.3 Beyond classical gravity: perturbative strings -- 1.4 Beyond perturbative strings: branes -- 1.5 The quantum dynamics of geometry -- 1.6 Things to do in the meantime -- 1.7 On with the show -- 2 Relativistic strings -- 2.1 Motion of classical point particles -- 2.1.1 Two actions -- 2.1.2 Symmetries -- 2.2 Classical bosonic strings -- 2.2.1 Two actions -- 2.2.2 Symmetries -- 2.2.3 String equations of motion -- 2.2.4 Further aspects of the two dimensional perspective -- 2.2.5 The stress tensor -- 2.2.6 Gauge fixing -- 2.2.7 The mode decomposition -- 2.2.8 Conformal invariance as a residual symmetry -- 2.2.9 Some Hamiltonian dynamics -- 2.3 Quantised bosonic strings -- 2.3.1 The constraints and physical states -- 2.3.2 The intercept and critical dimensions -- 2.3.3 A glance at more sophisticated techniques -- 2.4 The sphere, the plane and the vertex operator -- 2.4.1 States and operators -- 2.5 Chan-Paton factors -- 2.6 Unoriented strings -- 2.6.1 Unoriented open strings -- 2.6.2 Unoriented closed strings -- 2.6.3 World-sheet diagrams -- 2.7 Strings in curved backgrounds -- 2.8 A quick look at geometry -- 2.8.1 Working with the local tangent frames -- 2.8.2 Differential forms -- 2.8.3 Coordinate vs. orthonormal bases -- 2.8.4 The Lorentz group as gauge group -- 2.8.5 Fermions in curved spacetime -- 2.8.6 Comparison to differential geometry -- 3 A closer look at the world-sheet -- 3.1 Conformal invariance -- 3.1.1 Diverse dimensions -- 3.1.2 The special case of two dimensions -- 3.1.3 States and operators -- 3.1.4 The operator product expansion -- 3.1.5 The stress tensor and the Virasoro algebra.

3.2 Revisiting the relativistic string -- 3.3 Fixing the conformal gauge -- 3.3.1 Conformal ghosts -- 3.3.2 The critical dimension -- 3.4 The closed string partition function -- 4 Strings on circles and T-duality -- 4.1 Fields and strings on a circle -- 4.1.1 The Kaluza-Klein reduction -- 4.1.2 Closed strings on a circle -- 4.2 T-duality for closed strings -- 4.3 A special radius: enhanced gauge symmetry -- 4.4 The circle partition function -- 4.5 Toriodal compactifications -- 4.6 More on enhanced gauge symmetry -- 4.6.1 Lie algebras and groups -- 4.6.2 The classical Lie algebras -- 4.6.3 Physical realisations with vertex operators -- 4.7 Another special radius: bosonisation -- 4.8 String theory on an orbifold -- 4.9 T-duality for open strings: D-branes -- 4.9.1 Chan-Paton factors and Wilson lines -- 4.10 D-brane collective coordinates -- 4.11 T-duality for unoriented strings: orientifolds -- 5 Background fields and world-volume actions -- 5.1 T-duality in background fields -- 5.2 A first look at the D-brane world-volume action -- 5.2.1 World-volume actions from tilted D-branes -- 5.3 The Dirac-Born-Infeld action -- 5.4 The action of T-duality -- 5.5 Non-Abelian extensions -- 5.6 D-branes and gauge theory -- 5.7 BPS lumps on the world-volume -- 6 D-brane tension and boundary states -- 6.1 The D-brane tension -- 6.1.1 An open string partition function -- 6.1.2 A background field computation -- 6.2 The orientifold tension -- 6.2.1 Another open string partition function -- 6.3 The boundary state formalism -- 7 Supersymmetric strings -- 7.1 The three basic superstring theories -- 7.1.1 Open superstrings: type I -- 7.1.2 Closed superstrings: type II -- 7.1.3 Type I from type IIB, the prototype orientifold -- 7.1.4 The Green-Schwarz mechanism -- 7.2 The two basic heterotic string theories -- 7.2.1 SO(32) and E × E from self-dual lattices.

7.2.2 The massless spectrum -- 7.3 The ten dimensional supergravities -- 7.4 Heterotic toroidal compactifications -- 7.5 Superstring toroidal compactification -- 7.6 A superstring orbifold: discovering the K3 manifold -- 7.6.1 The orbifold spectrum -- 7.6.2 Another miraculous anomaly cancellation -- 7.6.3 The K3 manifold -- 7.6.4 Blowing up the orbifold -- 7.6.5 Some other K3 orbifolds -- 7.6.6 Anticipating D-manifolds -- 8 Supersymmetric strings and T-duality -- 8.1 T-duality of supersymmetric strings -- 8.1.1 T-duality of type II superstrings -- 8.1.2 T-duality of type I superstrings -- 8.1.3 T-duality for the heterotic strings -- 8.2 D-branes as BPS solitons -- 8.3 The D-brane charge and tension -- 8.4 The orientifold charge and tension -- 8.5 Type I from type IIB, revisited -- 8.6 Dirac charge quantisation -- 8.7 D-branes in type I -- 9 World-volume curvature couplings -- 9.1 Tilted D-branes and branes within branes -- 9.2 Anomalous gauge couplings -- 9.3 Characteristic classes and invariant polynomials -- 9.4 Anomalous curvature couplings -- 9.5 A relation to anomalies -- 9.6 D-branes and K-theory -- 9.7 Further non-Abelian extensions -- 9.8 Further curvature couplings -- 10 The geometry of D-branes -- 10.1 A look at black holes in four dimensions -- 10.1.1 A brief study of the Einstein-Maxwell system -- 10.1.2 Basic properties of Schwarzschild -- 10.1.3 Basic properties of Reissner-Nordstrom -- 10.1.4 Extremality, supersymmetry, and the BPS condition -- 10.1.5 Multiple black holes and multicentre solutions -- 10.1.6 Near horizon geometry and an infinite throat -- 10.1.7 Cosmological constant -- de Sitter and anti-de Sitter -- 10.1.8 de-Sitter spacetime and the sphere -- 10.1.9 Anti-de Sitter in various coordinate systems -- 10.1.10 Anti-de Sitter as hyperbolic slice -- 10.1.11 Revisiting the extremal solution -- 10.2 The geometry of D-branes.

10.2.1 A family of 'p-brane' solutions -- 10.2.2 The boost form of solution -- 10.2.3 The extremal limit and coincident D-branes -- 10.3 Probing p-brane geometry with Dp-branes -- 10.3.1 Thought experiment: building p with Dp -- 10.3.2 Effective Lagrangian from the world-volume action -- 10.3.3 A metric on moduli space -- 10.4 T-duality and supergravity solutions -- 10.4.1 D(p + 1) from Dp -- 10.4.2 D(p - 1) from Dp -- 11 Multiple D-branes and bound states -- 11.1 Dp and Dp ́from boundary conditions -- 11.2 The BPS bound for the Dp-Dp ́system -- 11.3 Bound states of fundamental strings and D-strings -- 11.4 The three-string junction -- 11.5 Aspects of D-brane bound states -- 11.5.1 0-0 bound states -- 11.5.2 0-2 bound states -- 11.5.3 0-4 bound states -- 11.5.4 0-6 bound states -- 11.5.5 0-8 bound states -- 12 Strong coupling and string duality -- 12.1 Type IIB/type IIB duality -- 12.1.1 D1-brane collective coordinates -- 12.1.2 S-duality and SL(2 ,Z ) -- 12.2 SO(32) Type I/heterotic duality -- 12.2.1 D1-brane collective coordinates -- 12.3 Dual branes from 10D string-string duality -- 12.3.1 The heterotic NS-fivebrane -- 12.3.2 The type IIA and type IIB NS5-brane -- 12.4 Type IIA/M-theory duality -- 12.4.1 A closer look at D0-branes -- 12.4.2 Eleven dimensional supergravity -- 12.5 E × E heterotic string/M-theory duality -- 12.6 M2-branes and M5-branes -- 12.6.1 Supergravity solutions -- 12.6.2 From D-branes and NS5-branes to M-branes and back -- 12.7 U-duality -- 12.7.1 Type II strings on T and E -- 12.7.2 U-duality and bound states -- 13 D-branes and geometry I -- 13.1 D-branes as probes of ALE spaces -- 13.1.1 Basic setup and quiver gauge theory -- 13.1.2 The moduli space of vacua -- 13.1.3 ALE space as metric on moduli space -- 13.1.4 D-branes and the hyper-Kähler quotient -- 13.2 Fractional D-branes and wrapped D-branes.

13.2.1 Fractional branes -- 13.2.2 Wrapped branes -- 13.3 Wrapped, fractional and stretched branes -- 13.3.1 NS5-branes from ALE spaces -- 13.3.2 Dual realisations of quivers -- 13.4 D-branes as instantons -- 13.4.1 Seeing the instanton with a probe -- 13.4.2 Small instantons -- 13.5 D-branes as monopoles -- 13.5.1 Adjoint Higgs and monopoles -- 13.5.2 BPS monopole solution from Nahm data -- 13.6 The D-brane dielectric effect -- 13.6.1 Non-Abelian world-volume interactions -- 13.6.2 Stable fuzzy spherical D-branes -- 13.6.3 Stable smooth spherical D-branes -- 14 K3 orientifolds and compactification -- 14.1 ZN orientifolds and Chan-Paton factors -- 14.2 Loops and tadpoles for ALE Z singularities -- 14.2.1 One-loop diagrams and tadpoles -- 14.2.2 Computing the one-loop diagrams -- 14.2.3 Extracting the tadpoles -- 14.3 Solving the tadpole equations -- 14.3.1 T-duality relations -- 14.3.2 Explicit solutions -- 14.4 Closed string spectra -- 14.5 Open string spectra -- 14.6 Anomalies for N = 1 in six dimensions -- 15 D-branes and geometry II -- 15.1 Probing p with D(p - 4) -- 15.2 Probing six-branes: Kaluza-Klein monopoles and M-theory -- 15.3 The moduli space of 3D supersymmetric gauge theory -- 15.4 Wrapped branes and the enhançon mechanism -- 15.4.1 Wrapping D6-branes -- 15.4.2 The repulson geometry -- 15.4.3 Probing with wrapped D6-brane -- 15.5 The consistency of excision in supergravity -- 15.6 The moduli space of pure glue in 3D -- 15.6.1 Multi-monopole moduli space -- 16 Towards M- and F-theory -- 16.1 The type IIB string and F-theory -- 16.1.1 SL(2,Z) duality -- 16.1.2 The (p,q) strings -- 16.1.3 String networks -- 16.1.4 The self-duality of D3-branes -- 16.1.5 (p,q) Fivebranes -- 16.1.6 SL(2,Z) and D7-branes -- 16.1.7 Some algebraic geometry -- 16.1.8 F-theory, and a dual heterotic description -- 16.1.9 (p,q) Sevenbranes.

16.1.10 Enhanced gauge symmetry and singularities of K3.