Table Of ContentSUPERSTRINGS
THE FIRST 15 YEARS flF SUPERSTRING THEORY • VOLUME 1
| EDITED BY JOHN H. SCHWARZ
World Scientific
SUPERSTRINGS
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SUPfRSTRMBS
IHE HRSf 15 YEARS Of SUPERSTRING THEORY* VOLUME 1
EDITEDBYJOHHH.SCHWARZ
Worid Scientific
L
Published by
World Scientific Publishing Co Pte Ltd.
P. O. Box 128, Fairer Road, Singapore 9128
242, Cherry Street, Philadelphia PA 19106-1906, USA
The editor and publisher are indebted to the authors and the following publishers
of the various journals and books for their assistance and permission to reproduce
the reprinted papers found in this volume: American Physical Society (Phys. Rev.
and Rev. Mod. Phys.); Harwood Academic Publishers GmBh (Surveys in High
Energy Physics); Kyoto University (Prog. Theor. Phys.); North-Holland Publishing
Co. (Nucl Phys., Phys. Lett, and Phys. Reports); Plenum Press (New frontiers in
High Energy Physics and Renormalization and Invariance in Quantum Field
Theory).
Library of Congress Cataloging in Publication Data
Main entry under title:
Superstrings: the first 15 years of superstring theory.
1. Superstring theories - Addresses, essays, lectures. 2. String models - Addresses,
essays, lectures. 3. Duality (Nuclear physics) - Addresses, essays, lectures. 4. Particles
(Nuclear physics) - Addresses, essays, lectures. I. Schwarz, John H.
QC794.6.S85S87 1985 539.7*54 85-11955
ISBN 9971-978-66-0
ISBN 9971-978-67-9 (pbk.)
Copyright © 1985 by World Scientific Publishing Co Pte Ltd.
All rights reserved. This book, or parts thereof, may not be reproduced
in any form or by any means, electronic or mechanical, including photo
copying, recording or any information storage and retrieval system now
known or to be invented, without written permission from the Publisher.
Printed in Singapore by Singapore National Printers (Pte) Ltd.
V
PREFACE
Superstring theory - or, more specifically, the £ x £ heterotic superstring - could
8 8
be a "theory of everything." It incorporates almost all fashionable ideas ranging from
axions and grand unification to supergravity and extra dimensions. It involves many
of the most beautiful and profound topics in mathematics. Most important of all, it
could be free from adjustable dimensionless parameters, finite, and realistic! Not
surprisingly, the recognition of this possibility has resulted in a great deal of excitement
and activity in the theoretical physics community.
Superstring theory has a bizarre history. It is an outgrowth of attempts to
describe hadrons and the strong interactions in the 1960's in terms of general princi
ples concerning the analytic S matrix. These ideas, despite their considerable
successes, were very controversial and even polarized the physics community to a cer
tain degree. Acceptance of superstrings as a candidate theory of elementary particle
physics at the Planck scale, first proposed in 1974, seems to have been delayed by a
decade due to the stigma associated with its origins.
Few theorists have previous experience in string theory or familiarity with the
literature on the subject. In view of the interest that now exists, it seems urgent to
make available a coherent presentation of the basic literature as quickly as possible.
That is the goal of these volumes. The student of string theory should not be put off
by their length. Many of the papers are mainly of historical significance. Others, such
as the ones on light-cone-gauge field theory in Chapters 10 and 11, develop approaches
whose importance for future developments is not yet clear. It is certainly possible, and
probably even desirable, to start doing research before mastering all the papers.
Let me apologize in advance to all who may feel that their contributions to the
development of string theory have been slighted in this presentation. The choice of
topics and papers undoubtedly reflects my own prejudices concerning what is impor
tant and relevant. In order not to make the volumes even longer I have chosen to
omit essentially all papers concerned only with bosonic strings (as opposed to super-
strings). A review article that discusses them is reprinted in Chapter 1, and other
review articles are also referenced. The papers in Chapter 10, which mainly concern
bosonic strings, are included because they have not been reviewed and are essential
background for Chapter 11. An active area of string-theory research that is only
touched on lightly concerns efforts to make sense of string theories for space-time
dimensions less than the critical one. The main motivation for such work is in con
nection with the original string program - namely, to describe four-dimensional hadron
physics. This is certainly a respectable enterprise, and deserves to be investigated, but
vi
it is not relevant to the main theme of these volumes - unification at the Planck scale.
Another factor that influenced the selection of papers is my familiarity and under
standing of them. Obviously, I am most familiar with my own papers, and it is
entirely possible that they are overrepresented despite an honest attempt to be objec
tive.
I wish to express my gratitude to my various collaborators - especially Andre'
Neveu, Joel Scherk, Lars Brink, and Michael Green - whose roles in the development
of superstring theory were absolutely essential. It is doubtful that the subject would
exist without them. I am indebted to Professor Murray Gell-Mann for his encourage
ment and support throughout the years in which superstrings were not fashionable. I
also wish to thank Professor K. K. Phua for proposing the publication of these
volumes and cooperating in bringing them to completion in a remarkably short time.
vii
CONTENTS
VOLUME 1
Preface v
Chapter 1 — REVIEW OF BOSONIC STRINGS 3
1. J. Scherk, "An Introduction to the Theory of Dual Models and Strings," 5
Rev. Mod. Phys. 47 (1975) 123-164.
Chapter 2 — THE ORIGINAL PAPERS 49
2. P. Ramond, "Dual Theory for Free Fermions," Phys. Rev. D3 (1971) 53
2415-2418.
3. A. Neveu and J. H. Schwarz, "Factorizable Dual Model of Pions," 57
NuclPhys. B31 (1971)86-112.
4. A. Neveu and J. H. Schwarz, "Quark Model of Dual Pions," 84
Phys. Rev. D4 (1971) 1109-1111.
5. A. Neveu, J. H. Schwarz, and C. B. Thorn, "Reformulation of the 87
Dual Pion Model," Phys. Lett. 35B (1971) 529-533.
Chapter3 —NO-GHOST THEOREMS AND DETERMINATION OF Z>= 10 95
6. J. H. Schwarz, "Physical States and Pomeron Poles in the Dual Pion 98
Model," Nucl. Phys. B46 (1972) 61-74.
7. P. Goddard and C. B. Thorn, "Compatibility of the Dual Pomeron with 112
Unitarity and the Absence of Ghosts in the Dual Resonance Model,"
Phys. Lett. 40B (1972) 235-238.
8. R. C. Brower and K. A. Friedman, "Spectrum-Generating Algebra 116
and No-Ghost Theorem for the Neveu-Schwarz Model," Phys. Rev. D7
(1973)535-539.
Vlll
9. L. Brink and H. B. Nielsen, "A Simple Physical Interpretation of the 121
Critical Dimension of Space-Time in Dual Models," Phys. Lett. 45B
(1973)332-336.
10. E. F. Corrigan and P. Goddard, "The Absence of Ghosts in the Dual 126
Fermion Model,"Nucl. Phys. B68 (1974) 189-202.
Chapter 4 —FERMION-EMISSION VERTEX AND FERMION-FERMION 143
SCATTERING
11. C. B. Thorn, "Embryonic Dual Model for Pions and Fermions," 145
Phys. Rev. DA (1971) 1112-1116.
12. L. Brink, D. Olive, C. Rebbi, and J. Scherk, "The Missing Gauge 150
Conditions for the Dual Fermion Emission Vertex and Their
Consequences,"Phys. Lett. 45B (1973) 379-383.
13. S. Mandelstam, "Manifestly Dual Formulation of the Ramond-Model," 155
Phys. Lett. 46B( 1973) 447-451.
14. J. H. Schwarz and C. C. Wu, "Evaluation of Dual Fermion Amplitudes," 160
Phys. Lett. 47B (1973) 453-456.
15. D. Bruce, E. Corrigan, and D. Olive, "Group Theoretical Calculation 164
of Traces and Determinants Occurring in Dual Theories," Nucl. Phys.
B95 (1975) 427-433.
Chapter 5 — TRANSITION FROM HADRONS TO ELEMENTARY 173
PARTICLES
16. T. Yoneya, "Connection of Dual Models to Electrodynamics and 176
Gravidynamics," Prog. Theor. Phys. 51 (1974) 1907-1920.
17. J. Scherk and J. H. Schwarz, "Dual Models for Non-hadrons," 191
Nucl. Phys. B81 (1974) 118-144.
18. J. Scherk and J. H. Schwarz, "Dual Model Approach to a 218
Renormalizable Theory of Gravitation," Honorable Mention in
the 1975 Gravitation Essay Contest of the Gravity Research
Foundation. Caltech preprint CALT-58-488 (unpublished). 5 pages.
19. J. Scherk and J. H. Schwarz, "Dual Field Theory of Quarks and 223
Gluons," Phys. Lett. 57B (1975 ) 463-466.
20. J. H. Sdiwarz, "Spinning String Theory from a Modern Perspective," 227
pp. 431-446 in Proc. Orbis Scientiae 1978, "New Frontiers in High-
Energy Physics," eds. A. Perlmutter and L. F. Scott (Plenum Press, 1978).
ix
Chapter 6 — WORLD-SHEET SUPERSYMMETRY 245
21. J. L. Gervais and B. Sakita, "Field Theory Interpretation of Supergauges 248
in Dual Models," Nucl Phys. B34 (1971) 632-639.
22. Y. Aharonov, A. Casher, and L. Susskind, "Spin-\ Partons in a Dual 256
Model of Hadrons,"/%ys. Rev. D5 (1972) 988-994.
23. B. Zumino, "Relativistic Strings and Supergauges," pp. 367-381 in 263
"Renormalization and Invariance in Quantum Field Theory," ed.
E. Caianiello (Plenum Press, 1974).
24. L. Brink, P. Di Vecchia, and P. Howe, "A Locally Supersymmetric and 278
Reparametrization Invariant Action for the Spinning String," Phys.
Lett. 65B (1976) 471-474.
25. S. Deser and B. Zumino, "A Complete Action for the Spinning String," 282
Phys. Lett. 65B (1976) 369-373.
26. A. M. Polyakov, "Quantum Geometry of Bosonic Strings," Phys. Lett. 287
103B (1981) 207-210.
27. A. M. Polyakov, "Quantum Geometry of Fermionic Strings," Phys. 291
Lett. 103B (1981) 211-213.
Chapter 7 — SPACE-TIME SUPERSYMMETRY 297
28. F. Gliozzi, J. Scherk, and D. Olive, "Supersymmetry, Supergravity 300
Theories and the Dual Spinor Model," Nucl Phys. Bl22 (1977 )
253-290.
29. M. B. Green and J. H. Schwarz, "Supersymmetrical Dual String 338
Theory," Nucl Phys. B181 (1981) 502-530.
30. M. B. Green and J. H. Schwarz, "Supersymmetrical String Theories," 367
Phys. Lett. 109B (1982) 444-448.
31. M. B. Green and J. H. Schwarz, "Covariant Description of Superstrings," 372
Phys. Lett. 136B (1984) 367-370.
Chapter 8 — DEVELOPMENT OF SUPERSTRING FORMALISM 379
32. M. B. Green and J. H. Schwarz, "Supersymmetric Dual String 382
Theory (II). Vertices and Trees," Nucl Phys. B198 (1982)
252-268.
