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M-Theory and Quantum Geometry : M-Theory and Quantum Geometry Proceedings of the NATO Advanced Study Institute on Quantum Geometry, Held in Akureyri, Iceland, on August 9-20, 1999 - Larus Thorlacius

M-Theory and Quantum Geometry

M-Theory and Quantum Geometry Proceedings of the NATO Advanced Study Institute on Quantum Geometry, Held in Akureyri, Iceland, on August 9-20, 1999

By: Larus Thorlacius (Editor), Thordur Jonsson (Editor)

Paperback Published: 30th September 2000
ISBN: 9780792364757
Number Of Pages: 454

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The fundamental structure of matter and spacetime at the shortest length scales remains an exciting frontier of basic research in theoretical physics. A unifying theme in this area is the quantization of geometrical objects. The majority of lectures at the Advanced Study Institute on Quantum Ge- ometry in Akureyri was on recent advances in superstring theory, which is the leading candidate for a unified description of all known elementary par- ticles and interactions. The geometric concept of one-dimensional extended objects, or strings, has always been at the core of superstring theory but in recent years the focus has shifted to include also higher-dimensional ob- jects, so called D-branes, which play a key role in the non-perturbative dynamics of the theory. A related development has seen the strong coupling regime of a given string theory identified with the weak coupling regime of what was previ- ously believed to be a different theory, and a web of such" dualities" that interrelates all known superstring theories has emerged. The resulting uni- fied theoretical framework, termed M-theory, has evolved at a rapid pace in recent years.

Prefacep. xi
D Branes in String Theory, I
Introductionp. 1
Perturbative String Theoryp. 2
Conformal Field Theory Formulationp. 11
T-Dualityp. 20
Classical Solutions Of The Low-Energy String Effective Actionp. 28
Bosonic Boundary Statep. 30
Fermionic Boundary Statep. 39
Classical Solutions From Boundary Statep. 46
Interaction Between a p and a p' Branep. 48
Moduli Spaces of Calabi-Yau Compactifications
Introductionp. 61
A short story about string theory, F-theory and M-theoryp. 61
String Theoryp. 61
Calabi-Yau compactificationsp. 63
String Dualitiesp. 64
F-Theoryp. 66
M-Theoryp. 67
Three Triplets of Dualitiesp. 68
The q = 16 tripletp. 68
The q = 8 tripletsp. 72
Calabi-Yau manifoldsp. 83
The M(atrix) Model of M-Theory
Introductionp. 91
Matrix theory from the quantized supermembranep. 92
Review of light-front stringp. 95
The bosonic membrane theoryp. 96
The light-front bosonic membranep. 98
Matrix regularizationp. 100
The bosonic membrane in a general backgroundp. 103
The supermembranep. 104
Covariant membrane quantizationp. 110
The BFSS conjecturep. 111
Membrane "instability"p. 112
M-theoryp. 114
The BFSS conjecturep. 115
Matrix theory as a second quantized theoryp. 116
Matrix theory and DLCQ M-theoryp. 118
M-theory objects from matrix theoryp. 123
Supergravitonsp. 123
Membranesp. 125
5-branesp. 133
Extended objects from matricesp. 137
Interactions in matrix theoryp. 139
Two-body interactionsp. 140
The N-body problemp. 156
Longitudinal momentum transferp. 160
Matrix theory in a general backgroundp. 160
T-dualityp. 161
Matrix theory on torip. 163
Matrix theory in curved backgroundsp. 165
Outlookp. 168
The Holographic Principle
Black Hole Complementarityp. 179
The Schwarzschild Black Holep. 180
Penrose Diagramsp. 184
Black Hole Thermodynamicsp. 185
The Thermal Atmospherep. 189
The Quantum Xerox Principlep. 190
Information Retention Timep. 192
Quantum Xerox Censorshipp. 194
Baryon Violation and Black Hole Horizonsp. 195
String Theory at High Frequencyp. 197
The Space Time Uncertainty Relationp. 199
Entropy Boundsp. 201
Maximum Entropyp. 201
Entropy on Light-Like Surfacesp. 203
Robertson Walker Geometryp. 205
Bousso's Generalizationp. 206
The AdS/CFT Correspondence and the Holographic Principlep. 210
AdS Spacep. 210
Holography in AdS Spacep. 211
The AdS/CFT Correspondencep. 212
The Infrared Ultraviolet Connectionp. 214
Counting Degrees of Freedomp. 215
AdS Black Holesp. 216
The Horizonp. 217
The Flat Space Limitp. 218
The Flat Space Limitp. 219
High Energy Gravitons Deep in the Bulkp. 220
Kaluza Klein Modesp. 222
Born-Infeld Actions and D-Brane Physics
D-Brane Solitons and the Born-Infeld Actionp. 227
Born-Infeld Dynamics of Branes in Flat Spacep. 231
Branes in Curved Space and the Gauge Theory Connectionp. 234
Born-Infeld Analysis of the Baryon Vertexp. 240
Applications of the AdS/CFT Correspondencep. 245
Summaryp. 252
Lectures on Superconformal Quantum Mechanics and Multi-Black Hole Moduli Spaces
Introductionp. 255
A Simple Example of Conformal Quantum Mechanicsp. 257
Conformally Invariant N-Particle Quantum Mechanicsp. 259
Superconformal Quantum Mechanicsp. 261
A Brief Diversion on Supergroupsp. 261
Quantum Mechanical Supermultipletsp. 263
Osp(1 2)-Invariant Quantum Mechanicsp. 264
D(2, 1; [alpha])-Invariant Quantum Mechanicsp. 267
The Quantum Mechanics of a Test Particle in a Reissner-Nordstrom Backgroundp. 271
Quantum Mechanics on the Black Hole Moduli Spacep. 274
The black hole moduli space metricp. 274
The Near-Horizon Limitp. 276
Conformal Symmetryp. 277
Discussionp. 278
Differential Geometry with Torsionp. 279
Large-N Gauge Theories
Introductionp. 285
O(N) Vector Modelsp. 286
Four-Fermi Interactionp. 287
Bubble graphs as zeroth order in 1/Np. 290
Scale and Conformal Invariance of Four-Fermi Theoryp. 292
Nonlinear sigma modelp. 297
Large-N factorization in vector modelsp. 300
Large-N QCDp. 300
Index or ribbon graphsp. 301
Planar and non-planar graphsp. 305
Topological expansion and quark loopsp. 312
Large-N[subscript c] factorizationp. 315
The master fieldp. 317
1/N[subscript c] as semiclassical expansionp. 319
QCD in Loop Spacep. 321
Observables in terms of Wilson loopsp. 322
Schwinger-Dyson equations for Wilson loopp. 324
Path and area derivativesp. 326
Loop equationsp. 330
Relation to planar diagramsp. 332
Loop-space Laplacian and regularizationp. 333
Survey of non-perturbative solutionsp. 337
Wilson loops in QCD[subscript 2]p. 338
Large-N Reductionp. 342
Reduction of scalar fieldp. 342
Reduction of Yang-Mills fieldp. 347
R[superscript d]-symmetry in perturbation theoryp. 349
Twisted reduced modelp. 350
Introduction to Random Surfaces
Introductionp. 355
Random pathsp. 356
Lattice pathsp. 357
Dynamically triangulated pathsp. 359
Branched polymersp. 362
Extrinsic propertiesp. 362
Intrinsic propertiesp. 366
Dynamicaly triangulated surfacesp. 368
Definitionsp. 368
Basic propertiesp. 369
The string tensionp. 370
Further resultsp. 372
Lattice surfacesp. 373
Definitionsp. 373
Critical behaviourp. 375
Conclusionp. 378
Lorentzian and Euclidean Quantum Gravity--Analytical and Numerical Results
Introductionp. 382
Lorentzian gravity in 2dp. 385
The discrete modelp. 385
The continuum limitp. 389
Topology changes and Euclidean quantum gravityp. 394
Baby universe creationp. 394
The fractal dimension of Euclidean 2d gravityp. 401
Euclidean quantum gravityp. 403
Some generalitiesp. 403
Dynamical triangulationsp. 404
The functional integralp. 407
Inclusion of matter fieldsp. 408
Numerical setupp. 410
Monte Carlo method and ergodic movesp. 410
Observables in 2d Euclidean gravityp. 417
Comments on the 2d resultsp. 428
Dynamically triangulated quantum gravity in d ] 2p. 433
Generalization to higher dimensionsp. 433
Numerical results in higher dimensionsp. 438
Outlookp. 442
Indexp. 451
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780792364757
ISBN-10: 0792364759
Series: NATO Science Series: U
Audience: General
Format: Paperback
Language: English
Number Of Pages: 454
Published: 30th September 2000
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 23.39 x 15.6  x 2.44
Weight (kg): 0.66