| Preface | p. xi |
| D Branes in String Theory, I | |
| Introduction | p. 1 |
| Perturbative String Theory | p. 2 |
| Conformal Field Theory Formulation | p. 11 |
| T-Duality | p. 20 |
| Classical Solutions Of The Low-Energy String Effective Action | p. 28 |
| Bosonic Boundary State | p. 30 |
| Fermionic Boundary State | p. 39 |
| Classical Solutions From Boundary State | p. 46 |
| Interaction Between a p and a p' Brane | p. 48 |
| Moduli Spaces of Calabi-Yau Compactifications | |
| Introduction | p. 61 |
| A short story about string theory, F-theory and M-theory | p. 61 |
| String Theory | p. 61 |
| Calabi-Yau compactifications | p. 63 |
| String Dualities | p. 64 |
| F-Theory | p. 66 |
| M-Theory | p. 67 |
| Three Triplets of Dualities | p. 68 |
| The q = 16 triplet | p. 68 |
| The q = 8 triplets | p. 72 |
| Calabi-Yau manifolds | p. 83 |
| The M(atrix) Model of M-Theory | |
| Introduction | p. 91 |
| Matrix theory from the quantized supermembrane | p. 92 |
| Review of light-front string | p. 95 |
| The bosonic membrane theory | p. 96 |
| The light-front bosonic membrane | p. 98 |
| Matrix regularization | p. 100 |
| The bosonic membrane in a general background | p. 103 |
| The supermembrane | p. 104 |
| Covariant membrane quantization | p. 110 |
| The BFSS conjecture | p. 111 |
| Membrane "instability" | p. 112 |
| M-theory | p. 114 |
| The BFSS conjecture | p. 115 |
| Matrix theory as a second quantized theory | p. 116 |
| Matrix theory and DLCQ M-theory | p. 118 |
| M-theory objects from matrix theory | p. 123 |
| Supergravitons | p. 123 |
| Membranes | p. 125 |
| 5-branes | p. 133 |
| Extended objects from matrices | p. 137 |
| Interactions in matrix theory | p. 139 |
| Two-body interactions | p. 140 |
| The N-body problem | p. 156 |
| Longitudinal momentum transfer | p. 160 |
| Matrix theory in a general background | p. 160 |
| T-duality | p. 161 |
| Matrix theory on tori | p. 163 |
| Matrix theory in curved backgrounds | p. 165 |
| Outlook | p. 168 |
| The Holographic Principle | |
| Black Hole Complementarity | p. 179 |
| The Schwarzschild Black Hole | p. 180 |
| Penrose Diagrams | p. 184 |
| Black Hole Thermodynamics | p. 185 |
| The Thermal Atmosphere | p. 189 |
| The Quantum Xerox Principle | p. 190 |
| Information Retention Time | p. 192 |
| Quantum Xerox Censorship | p. 194 |
| Baryon Violation and Black Hole Horizons | p. 195 |
| String Theory at High Frequency | p. 197 |
| The Space Time Uncertainty Relation | p. 199 |
| Entropy Bounds | p. 201 |
| Maximum Entropy | p. 201 |
| Entropy on Light-Like Surfaces | p. 203 |
| Robertson Walker Geometry | p. 205 |
| Bousso's Generalization | p. 206 |
| The AdS/CFT Correspondence and the Holographic Principle | p. 210 |
| AdS Space | p. 210 |
| Holography in AdS Space | p. 211 |
| The AdS/CFT Correspondence | p. 212 |
| The Infrared Ultraviolet Connection | p. 214 |
| Counting Degrees of Freedom | p. 215 |
| AdS Black Holes | p. 216 |
| The Horizon | p. 217 |
| The Flat Space Limit | p. 218 |
| The Flat Space Limit | p. 219 |
| High Energy Gravitons Deep in the Bulk | p. 220 |
| Kaluza Klein Modes | p. 222 |
| Born-Infeld Actions and D-Brane Physics | |
| D-Brane Solitons and the Born-Infeld Action | p. 227 |
| Born-Infeld Dynamics of Branes in Flat Space | p. 231 |
| Branes in Curved Space and the Gauge Theory Connection | p. 234 |
| Born-Infeld Analysis of the Baryon Vertex | p. 240 |
| Applications of the AdS/CFT Correspondence | p. 245 |
| Summary | p. 252 |
| Lectures on Superconformal Quantum Mechanics and Multi-Black Hole Moduli Spaces | |
| Introduction | p. 255 |
| A Simple Example of Conformal Quantum Mechanics | p. 257 |
| Conformally Invariant N-Particle Quantum Mechanics | p. 259 |
| Superconformal Quantum Mechanics | p. 261 |
| A Brief Diversion on Supergroups | p. 261 |
| Quantum Mechanical Supermultiplets | p. 263 |
| Osp(1 2)-Invariant Quantum Mechanics | p. 264 |
| D(2, 1; [alpha])-Invariant Quantum Mechanics | p. 267 |
| The Quantum Mechanics of a Test Particle in a Reissner-Nordstrom Background | p. 271 |
| Quantum Mechanics on the Black Hole Moduli Space | p. 274 |
| The black hole moduli space metric | p. 274 |
| The Near-Horizon Limit | p. 276 |
| Conformal Symmetry | p. 277 |
| Discussion | p. 278 |
| Differential Geometry with Torsion | p. 279 |
| Large-N Gauge Theories | |
| Introduction | p. 285 |
| O(N) Vector Models | p. 286 |
| Four-Fermi Interaction | p. 287 |
| Bubble graphs as zeroth order in 1/N | p. 290 |
| Scale and Conformal Invariance of Four-Fermi Theory | p. 292 |
| Nonlinear sigma model | p. 297 |
| Large-N factorization in vector models | p. 300 |
| Large-N QCD | p. 300 |
| Index or ribbon graphs | p. 301 |
| Planar and non-planar graphs | p. 305 |
| Topological expansion and quark loops | p. 312 |
| Large-N[subscript c] factorization | p. 315 |
| The master field | p. 317 |
| 1/N[subscript c] as semiclassical expansion | p. 319 |
| QCD in Loop Space | p. 321 |
| Observables in terms of Wilson loops | p. 322 |
| Schwinger-Dyson equations for Wilson loop | p. 324 |
| Path and area derivatives | p. 326 |
| Loop equations | p. 330 |
| Relation to planar diagrams | p. 332 |
| Loop-space Laplacian and regularization | p. 333 |
| Survey of non-perturbative solutions | p. 337 |
| Wilson loops in QCD[subscript 2] | p. 338 |
| Large-N Reduction | p. 342 |
| Reduction of scalar field | p. 342 |
| Reduction of Yang-Mills field | p. 347 |
| R[superscript d]-symmetry in perturbation theory | p. 349 |
| Twisted reduced model | p. 350 |
| Introduction to Random Surfaces | |
| Introduction | p. 355 |
| Random paths | p. 356 |
| Lattice paths | p. 357 |
| Dynamically triangulated paths | p. 359 |
| Branched polymers | p. 362 |
| Extrinsic properties | p. 362 |
| Intrinsic properties | p. 366 |
| Dynamicaly triangulated surfaces | p. 368 |
| Definitions | p. 368 |
| Basic properties | p. 369 |
| The string tension | p. 370 |
| Further results | p. 372 |
| Lattice surfaces | p. 373 |
| Definitions | p. 373 |
| Critical behaviour | p. 375 |
| Conclusion | p. 378 |
| Lorentzian and Euclidean Quantum Gravity--Analytical and Numerical Results | |
| Introduction | p. 382 |
| Lorentzian gravity in 2d | p. 385 |
| The discrete model | p. 385 |
| The continuum limit | p. 389 |
| Topology changes and Euclidean quantum gravity | p. 394 |
| Baby universe creation | p. 394 |
| The fractal dimension of Euclidean 2d gravity | p. 401 |
| Euclidean quantum gravity | p. 403 |
| Some generalities | p. 403 |
| Dynamical triangulations | p. 404 |
| The functional integral | p. 407 |
| Inclusion of matter fields | p. 408 |
| Numerical setup | p. 410 |
| Monte Carlo method and ergodic moves | p. 410 |
| Observables in 2d Euclidean gravity | p. 417 |
| Comments on the 2d results | p. 428 |
| Dynamically triangulated quantum gravity in d ] 2 | p. 433 |
| Generalization to higher dimensions | p. 433 |
| Numerical results in higher dimensions | p. 438 |
| Outlook | p. 442 |
| Index | p. 451 |
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