Strings, Branes and Dualities

490 Pages·1999·15.862 MB·English

by  David I. Olive (auth.), Laurent Baulieu, Philippe Di Francesco, Michael Douglas, Vladimir Kazakov, Marco Picco, Paul Windey (eds.)

Strings, Branes and Dualities
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Series C: Mathematical and Physical Sciences - Vol. 520
Strings, Branes and Dualities
edited by
Laurent Baulieu
CNRS and Universite Pierre et Marie Curie (Paris VI).
Paris. France
Philippe Di Francesco
University of North Carolina at Chapel Hill.
Chapel HiII. NC. U.S.A.
Michael Douglas
Rutgers University.
Piscataway. NJ. U.S.A.
and Institut des Hautes Etudes Scientifiques.
Bures-sur-Yvette. France
Vladimir Kazakov
Universite Pierre et Marie Curie (Paris VI).
and Ecole Normale Superieure.
Paris. France
Marco Picco
CNRS and Universite Pierre et Marie Curie (Paris VI).
Paris. France
and
Paul Windey
Universite Pierre et Marie Curie (Paris VI).
Paris. France
Springer Science+Business Media, B.V.
Proceedings of the NATO Advanced Study Institute on
Strings, Branes and Dualities
Cargese, France
May 26-June 14, 1997
A C.I.P. Catalogue record for this book is available from the Library of Congress.
ISBN 978-94-010-5989-3 ISBN 978-94-011-4730-9 (eBook)
DOI 10.1007/978-94-011-4730-9
Printed on acid-free paper
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© 1999 Springer Science+Business Media Dordrecht
Originally published by Kluwer Academic Publishers in 1999
Softcover reprint of the hardcover 1st edition 1999
No part of the material protected by this copyright notice may be reproduced or
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permission from the copyright owner.
Table of Contents
Preface xi
I Lectures 1
EXACT ELECTROMAGNETIC DUALITY 3
by DA VID I OLIVE
1 Introduction ............. . 3
2 Unified Gauge Theories ...... . 8
3 Electromagnetic Duality Conjectures 13
4 Algebraic Structure of Supersymmetry 16
5 Supersymmetry to the Rescue ..... 21
6 Electromagnetic Duality and the Modular Group 25
SUPERSYMMETRY AND DUALITIES
IN VARIOUS DIMENSIONS 33
by BERNARD DE WIT AND JAN LOUIS
1 Introduction .............. . 33
2 Supersymmetry in various dimensions 34
2.1 The supersymmetry algebra .. 35
2.2 Massless representations .... 36
2.3 Maximal supersymmetry: Q ~ 32 . 44
2.4 Maximal supergravities ..... . 45
2.5 Dimensional reduction and hidden symmetries 51
2.6 Nonmaximal supersymmetry ..... 58
3 String theories in various dimensions . . . . . . . . . . 61
=
3.1 Perturbative string theories in D 10 . . . . . 61
3.2 Calabi-Yau compactifications and perturbative dualities. 66
3.3 Duality in string theory 77
A Field representations . . . . . . . . . . . . 88
A.l Graviton fields .......... . 88
A.2 Antisymmetric tensor gauge fields 89
A.3 Spinor fields. . . . . . . . . . . . . 90
A.4 Gravitino fields . . . . . . . . . . . 91
B Coupling constants of low-energy effective field theories 91
vi
SElBERG-WITTEN THEORY AND S-DUALITY 103
by TOHRU EGUCHI
1 Introduction.............. 103
2 8U(2) gauge theory without matter 105
3 8U(2) gauge theory with matter .. 110
4 4-dimensional conformal field theory 117
DUALITIES IN THE CLASSICAL
SUPERGRAVITY LIMITS 121
by B. L. JULIA
1 Introduction. 121
2 Silver rules . 124
3 Dualisations . 129
4 Higher order potentials. 132
5 Complementarity, dyons, TS and F -duality and conclusion . 136
M-THEORY FROM ITS SUPERALGEBRA 141
by P.K. TOWNSEND
Lecture 1: M-branes and supersymmetry . 141
Lecture 2: More branes from M-theory . 150
Lecture 3: Dualities ...... . 155
Lecture 4: Intersecting M-branes 164
Epilogue ............. . 174
LECTURES ON HETEROTIC-TYPE I DUALITY 179
by I. A NTONIADIB, H. PARTOUCHE AND T.R. TAYLOR
1 Introduction.......... 179
2 Type I Strings and D-Branes ........ . 180
3 Effective Field Theories . . . . . . . . . . . . 182
4 Type I-Heterotic Duality in Six Dimensions . 184
5 Type I-Heterotic Duality in Four Dimensions 186
6 One-loop Corrections. . . . . . . . . . 189
7 Example of Type I-Heterotic Duality. 191
7.1 Higgs Phase .... 191
7.2 Coulomb Phase . . 192
8 Higher-derivative F-terms 195
CONNECTIONS BETWEEN M-THEORY
AND SUPERSTRINGS 201
by MICHAEL B. GREEN
1 Introduction ................... . 201
2 Higher-order terms in M-theory ........ . 203
2.1 8L{2, Z)-invariant R4 terms in type IIB 203
2.2 One loop in eleven dimensions .... . 205
2.3 Sixteen-fermion and related terms .. . 208
3 Tree-level string theory and multi-loop supergravity. 210
vii
A Momentum dependence of one-loop amplitude. 214
BLACK HOLES AND D-BRANES 219
by JUAN M. MALDACENA
1 Introduction ................... . 219
2 Classical solutions ............... . 220
3 D-brane description of extremal 5d black holes 223
3.1 Description in terms of open strings 223
3.2 Description in terms of instantons 226
3.3 A more geometric picture . . . . . 227
3.4 Justification of the BPS counting . 228
4 Near Extremal black holes. 229
5 Greybody factors 234
6 Final remarks ....... . 237
M-THEORY AND N = 2 STRINGS 241
by EMIL MARTINEC
1 Introduction ..................... . 241
2 (2,2) Strings ..................... . 244
2.1 Open strings, D-branes, and matrix theory 247
3 (2,1) Strings .................... . 249
3.1 Toroidal compactification of (2,1) strings . 252
3.2 Heterotic/type I construction ....... . 253
4 S-matrix, effective action and geometry of (2,1) strings. 255
5 Connections between (2,1) strings and matrix theory. 257
A Technology of local N=2 worldsheet supersymmetry 260
B (2,2) open strings and D-branes ....... . 261
B.1 Boundary conditions and D-branes .. 262
B.2 Coupling D-branes to self-dual gravity 263
BRANES WITHIN BRANES 267
by MICHAEL R. DOUGLAS
1 Introduction........ 267
2 RR fields in superstring theory 268
3 Branes in type I theory 270
4 Branes within branes . . . . . . 271
REVIEW OF MATRIX THEORY 277
by D. BIGATTI AND L. SUSSKIND
Lecture zero: Introduction ... . 277
Lecture 1: The light cone frame .. . 278
1.1 DLCQ ......... . 282
1.2 Another view of DLCQ 283
1.3 Supergalilean symmetry 284
Lecture 2: Matrix theory. . . . . . . 285
2.1 Type IIA string theory and M theory 285
viii
2.2 DLCQ of M-theory . . . . . . . 288
2.3 DO-brane quantum mechanics. 288
2.4 The supergraviton . . . . . . . 291
Lecture 3: Objects and dualities in Matrix theory . 298
3.1 2-branes and 5-branes 298
3.2 Compactification............ 301
3.3 T -duality . . . . . . . . . . . . . . . . 304
Lecture 4: The emergence of space in Matrix theory 306
4.1 Supergraviton scattering with exchange of Py . 308
Lecture 5: Black holes in matrix theory ...... . 310
5.1 Choosing N ............... . 310
5.2 Properties of Schwartzschild black holes 311
5.3 Super Yang Mills thermodynamics 312
5.4 Black hole thermodynamics 313
5.5 Low temperatures ........ . 315
NOTES ON MATRIX AND MICRO STRINGS 319
by R. DIJKGRAAF, E. VERLINDE AND H. VERLINDE
1 Introduction.......... 319
2 U-duality and the M5-brane . 321
3 BPS Spectrum . . . . . . . 324
4 M-theory from NS 5-branes 327
5 SYM theory on T5 . . 331
6 Winding Microstrings .., 333
7 The Matrix M5-brane ... 335
8 SN Orbifolds and 2nd Quantized Strings. 337
9 String Interactions via Twist Fields . 340
10 Matrix String Theory . 342
11 Microstring Interactions 346
12 Future Directions . . . . 350
II Seminars 357
TESTING SElBERG-WITTEN SOLUTION 359
by A. LOSEV, N. NEKRASSOV AND S. SHATASHVILI
1 Introduction and summary ... 359
2 The micro/macroscopic theories . 360
3 Coulomb branch measure . . . . 363
3.1 Low-energy theory .... 364
3.2 Specific computations of the contact terms 368
3.3 Contact term of O-observables and 4-observables 369
4 Remarks on ADHM integration . . . . . . . . . . . . . . 370
ix
MIRRORS AND PHASES OF N=4 IN D=3 373
by ZHENG YIN
1 Introduction .......... . 373
2 What is 3d Mirror Symmetry? 373
3 Set the Branes to work. 378
4 Mirror Pairs . . . . . . . 381
5 Phases and Transitions. 383
INTERSECTION RULES AND OPEN BRANES 387
by RICCARDO ARGURIO
1 Introduction............................ 387
2 The Harmonic Superposition and the Intersection Rules . . . 388
3 Intersections in String and M-theory and Black Hole Entropy 391
4 When the Intersection is Actually a Boundary. . . . . . . . . 392
HOW TO COUNT THE STATES OF EXTREMAL
BLACK HOLES IN N=8 SUPERGRAVITY 399
by VIJAY BALASUBRAMANIAN
1 Introduction ................. . 399
=
2 Black Hole Entropy in N 8 Supergravity 400
2.1 Generating Solutions ...... . 401
3 Supersymmetry and Branes at Angles . 402
3.1 2-branes at Angles and 6-branes 403
4 Classical Solutions for Branes at Angles 404
5 Counting the States of Our Black Holes 406
6 Discussion: 5 Parameter Generating Solution 408
ASPECTS OF D-INSTANTONS 411
by MICHAEL GUTPERLE
1 Introduction ......... . 411
2 IIB supergravity ...... . 412
3 D-instanton in IIB supergravity . 412
4 Instanton induced interactions 413
5 Modular Invariance ....... . 416
6 One loop in eleven dimensions. . 417
A One point functions in the upper half plane 418
A.l Dilatino ............. . 419
A.2 NS 0 NS antisymmetric tensor . 419
A.3 R 0 R antisymmetric tensor 420
A.4 Graviton........ 420
SOME CLASSICAL SOLUTIONS
OF MEMBRANE MATRIX MODEL EQUATIONS 423
by JENS HOPPE
x
III Gong Show 429
D-BRANE ACTIONS, INTRINSIC GEOMETRY
AND DUALITY 431
by M. ABOU ZEID
BRANES AND CHIRAL SYMMETRY 437
by J.H. BRODIE
REGULARISATION OF CLASSICAL SELF INTERACTION
IN STRINGS 441
by B. CARTER
D-BRANE BOUND STATES 445
by MIGUEL S. COSTA
SPECIAL K.AHLER GEOMETRY 449
by B. CRAPS, F. ROOSE, W. TROOST AND A. VAN PROEYEN
COMPACTIFICATION OF M-THEORY
AND SUSY BREAKING 455
by C. GROJEAN
THREEBRANES IN TWELVE DIMENSIONS 459
by S. F. HEWSON
STRING SOLITONS AND DIMENSIONAL REDUCTION 463
by GERMAR SCHRODER
BPS SATURATED AMPLITUDES
AND NON-PERTURBATIVE STRING THEORY 467
by PIERRE VANHOVE
ON DOMAIN WALL IN MQCD 471
by ANASTASIA VOLOVICH
Appendix 475
KIDS WALKING ON A D-BRANE 477
Interviews by NINA ILIEVA-DOUGLAS
LIST OF SPEAKERS 485
LIST OF PARTICIPANTS 487
INDEX 491