Abstract
When I originally agreed to accept the kind invitation to lecture at the NATO Summer School in Cargese, my topic was to be the theory of CP violation. The developments of the past year have resulted in growing interest in the theory of superstrings, a subject which is on the one hand extraordinarily exciting in the promise it holds for solutions of many of the outstanding problems of particle physics and on the other hand rather forbidding in the amount of new knowledge which needs to be acquired by the average theorist to understand the papers that are now being published on the recent developments. These considerations have persuaded me “in extremis”, to change the subject of my lectures.
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Reference
Chapter 2
Some recent reviews on string theory are listed below : J.H. Schwarz, Phys. Rep. 89 (1982) 223
M.B. Green, Surveys in High Energy Physics 3 (1982) 127
L. Brink “Superstrings”, CERN TH 4006/84.
The World Scientific Press (Singapore) has announced publication in December of three books which should be helpful in bringing the reader up to date. They are :
J.H. Schwarz, Superstrings;
Unified String Theories, Proceedings of the Santa Barbara Workshop, Aug. 1985, eds. M.B. Green and D.J. Gross;
Yale Summer School on High Energy Physics, June 1985, eds.F. Gursey and M. Bowick. This is not the place to try to give references to the new literature on string theories.
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Chapter 3
H. Flanders, “Differential Forms” New York, Academic Press (publ.) 1963.
T. Eguchi, P. Gilkey and A.J. Hanson, Phys. Rep. 66 (1980) 213.
See also references in ch. 4 to gravitational anomalies for general introduction to Riemannian geometry as well as ref. [2] cited above.
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Chapter 4
Three recent references on gauge field anomalies are : B. Zumino “Chiral Anomalies and Differential Geometry” in Relativity Groups and Topology (B.S. De Witt and R. Stora, eds.) North Holland, 1983
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L. Alvarez-Gaume and E. Witten, Nucl. Phys. B234 (1984) 269.
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E. Witten, Phys. Lett. 149B (1984) 351.
E. Witten, “Global Gravitational Anomalies”, “Global Anomalies in String Theory”, Princeton University Preprints (1985).
Chapter 5
A good general reference is J. Wess and J. Bagger, “Supersymmetry and Supergravity”, Princeton University Press (1983).
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Chaper 6
We are following here R.N. Mohapatra and B. Sakita, Phys. Rev. D21 (1980) 1062.
Clearly it is awkward to define Γ 1,2=t2,1 rather than Γ1,2 = 2 but we wish to display an explicit’form For the Γ matrices’keeping the notation of ref. [1]. It would have been preferable to exchange Γ2i_1 and Γ2i-in (6.7).
A quick summary of E6, branching rules, etc. is contained in R. Slansky, Phys. Rep. 79 (1981) 1.
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Chapter 7
Z. Horvath and L. Palla, Nucl. Phys. B142 (1978) 327
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E. Witten, Nucl. Phys. B186 (1981) 412.
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G. Chapline and N. Manton, Nucl. Phys. B184 (1981) 391
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E. Witten, Proceedings of Shelter Island II, p. 227 (published by M.I.T. Press, 1985).
Some representative references are :
M. Gell-Mann, P. Ramond and R. Slansky in “Supergravity” ed. P. Van Nieuwenhuizen and D.Z. Freedman (North Holland, 1979);
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J. Kim, Phys. Rev. Lett. 45 (1980) 1916;
H. Sato, Phys. Rev. Lett. 45 (1980) 1997;
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E. Witten, J. Diff. Geom. 17 (1982) 661.
See for a review S. Coleman, “The Uses of Instantons” in “Lectures on Field Theory”, Oxford University press (1985).
See ref. [2], ch. 3 for a detailed discussion of index theorem. Other good references are Luis Alvarez-Gaume, “Supersymmetry and Index Theory”, Lectures at Bonn Summer School 1984, to be published; J. Manes and B. Zumino, LBL-20234 preprint 1985
L. Alvarez-Gaume, Math. Phys. 90 (1983) 161
D. Friedan and P. Windey, Nucl. Phys. B235 (1984) 295.
B. Zumino, Proceedings of Shelter Island II, p. 79 (published by M.I.T. Press, 1985).
Chapter 8
Ch. 5, reference [7].
CHSW stands for P. Candelas, G. Horowitz, A. Strominger and E. Witten, Nucl. Phys. B258 (1985) 46.
Alternative schemes have been considered, following CHSW. For ins-tance, manifolds with non-vanishing H have been considered by I. Bars, Phys. Rev. D33 (1986) 383; mnpI. Bars, D. Nemeschansky and S. Yankielowicz, “Torsion in Super-strings” SLAC-Pub 3758 (1985).
E. Calabi in Algebraic Geometry and Topology : A Symposium in Honor of S. Lefshetz (Princeton University Press) 1957
S.T. Yau, Proc. Nat. Acad. Sci. 74 (1978) 177.
K. Uhlenbeck and S.T. Yau, to be published, presents an analysis of this equation.
For a detailed discussion which does not assume identification of the spin connection and SU(3) gauge fields, see I. Bars and M. Visser, “Number of Massless Fermion Fields in Superstring Theory”, Univ. of So. Calif, preprint 85/016 (1985). See also R. Nepomechie, Y.S. Wu and A. Zee, Phys. Lett. 158B (1975) 311.
E. Witten, Nucl. Phys. B258 (1985) 75.
E. Witten, “New Issues in Manifolds of SU(3) Holonomy”, Princeton preprint 1985.
A. Strominger and E. Witten, “New Manifolds for Superstring Compactification”, Princeton preprint.
Chapter 9
We are following here again P. Candelas et al., ref. [2] of chapter 8.
E. Witten, Nucl. Phys. B258 (1985) 75.
J.D. Breit, B.A. Ovrut and G. Segrè, Phys. Lett. 158B (1985) 33
A. Sen, Phys. Rev. Lett. 55 (1985) 33.
Y. Hosotani, Phys. Lett. 126B (1983) 303.
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M. Dine, V. Kaplunovsky, M. Mangano, C. Nappi and N. Seiberg, “Superstring Model Building”, Nucl. Phys. B259 (1985) 543.
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See for example, A. Strominger and E. Witten, “New Manifolds for Superstring Compactification”, Princeton (1985) to be published in Nucl. Phys. A. Strominger “Yukawa Couplings in Superstring Compactification” ITP (Santa Barbara) preprint (1985).
For a good recent discussion of the overall picture see : J.P. Derendinger, L.E. Ibanez and H.P. Nilles, “On the Low Energy Limit of Superstring Theories”, CERN Th 4228 preprint (1985).
Chapter 10
E. Witten, “Dimensional Reduction of Superstring models”, Princeton preprint. Phys. Lett. 155B (1985) 151.
E. Witten, Ref. [5], section 2.
E. Cremmer, S. Ferrara, L. Girardello and A. Von Proeyen, Phys. Lett. 116B (1982) 231
E. Cremmer, S. Ferrara, L. Girardello and A. Von Proeyen, Nucl. Phys. B212 (1983) 412
E. Cremmer, B. Julia, J. Scherk, S. Ferrara, L. Girardello and P. Van Nieuwenhuizen, Nucl. Phys. B147 (1979) 105.
The formulation in terms of Kähler geometry is given in : J. Bagger and E. Witten, Phys. Lett. 115B (1982) 202
J. Bagger and E. Witten, Phys. Lett. 118B (1982) 303
J. Bagger and E. Witten, J. Bagger, Nucl. Phys. B211 (1983) 302.
We have followed reference [1] so far. This form of Kähler potential was independently shown to arise in the analysis of so-called 16/16 supergravity models, cf. W. Lang, J. Louis and B. Ovrut, Univ. of Penn., preprint UPR-0280T (1985) and Karlsruhe preprint KA-THE P 85-2 (1985). See also earlier references to G. Girardi, R. Grimm, M. Muller and J. Wess, Z. Phys. C26 (1986) 123; C26 (1984) 427; Phys. Lett. 147B (1984) 81. It is interesting to speculate on which of these two paths is a more realistic approximation to superstring phenomena.
J.P. Derendinger, L.I. Ibanez and H.P. Nilles, ref. [10], section 9.
Chapter 11
J.P. Derendinger, L.E. Ibanez and H.P. Nilles, Phys. Lett. 155B (1985) 65.
M. Dine, R. Rohm, N. Seiberg and E. Witten, Phys. Lett. 156B (1985) 55.
J.P. Derendinger, L.I. Ibanez and H.P. Nilles, “On the Low Energy Limit of Superstring Theories”, CERN -TH. 4228/85 preprint.
For a recent discussion see R. Rohm and E. Witten, “The Antisymmetric Tensor Field in Superstring Theory” Princeton University preprint (Nov. 1985). See also R. Nepomechie, Y.S. Wu and A. Zee, Phys. Lett. 158B (1985) 311.
E. Witten, ref. [1], ch. 10.
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This section is a condensed version of J.D. Breit, B.A. Ovrut and G. Segrè, Phys. Lett. 162B (1985) 303.
S. Coleman and E. Weinberg, Phys. Rev. D7 (1983) 2369.
For complete references, see e.g. H.P. Nilles, Phys. Rep. 110 (1984) 1. Some papers are : J. Polonyi, Budapest preprint K-FK1–38 (1977)
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For recent examples, see e.g. M. Cvetic and C. Preitschopf, SLAC-PUB-3685 (1985)
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M. Srednicki and S. Theisen, UCSB preprint.
P. Binetruy and M.K. Gaillard, “Radiative Corrections in Compactified Superstring Models” LBL-19972 preprint (1985).
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Chapter 12
For early references, see ch. 9, refs. [8–10]. Among more recent works, a sample is given by V. Kaplunosky and C. Nappi, “Phenomenological Implications of Superstring Theory”, Princeton preprint 1985; P. Binetruy, S. Dawson, I. Hinchcliffe and M. Sher, “Phenomenologically Viable Models from Superstrings”. E. Cohen, J. Ellis; K. Enqvist and D.V. Nanopoulos, CERN TH preprints 4222/85, 4195/85; R. Holman and D.B. Reiss, “Fermion Masses in E8 x E8 Superstring Theories”, Fermilab. preprint 1985; T. Hubsch, H. Nishino and J.G. Pati, “Do Superstrings Lead to Preons”, to appear in Phys. Lett. B.; C.P. Burgess, A. Foni and F. Quevedo, “Low Energy Effective Action for the Superstring”, Univ° of Texas Preprint; R.N. Mohapatra, “A mechanism for Understanding Small Neutrino Masses in SUSY Theories”, Univ. of Maryland preprint (1985); S. Nandi and U. Sarkar, Univ. of Texas Preprint (1985).
K. Choi and J.E. Kim, Phys. Lett. 154B (1985) 393; S.M. Barr, Phys. Lett. 154B (1985) 397; K. Yamamoto, Univ. of No. Carolina preprint (1985); K. Choi and J.E. Kim, Seoul preprint SNUHE 85/10; M. Dine and N. Seiberg, “String Theory and the Strong CP Problem”, CUNY preprint 1985; X.G. Wen and E. Witten, “World Sheet Instantons and the Peccei-Quinn Symmetry”, Princeton preprint. [3] M.J. Bowick, L. Smolin and L.C.R. Widjewardhana, Phys. Rev. Lett. 56 (1986) 424; J. Lazarides, G. Panagiotakopoulos and Q. Shafi, Phys. Rev. Lett. 56 (1986) 432 and Bartol preprint BA-85 “Baryogenesis and the Gravitino Problem in Superstring Theories”; J.A. Stein-Schabes and M. Gleiser, “Low Energy Superstring Cosmology”, Fermilab preprint 1985; R. Holman and T. Kephart, “Axion Cosmology in Automatic E6 x U(l) Models”, Fermilab pub, 85/117; E.W. Kolb, D. Seckel and M.S. Turner, “The Shadow World”, Fermilab preprint.
See e.g., M. Evans and B.A. Ovrut, “Splitting the Superstring Vacuum Degeneracy”, Rockefeller preprint 1985.
L. Dixon, J.A. Harvey, C. Vafa and E. Witten, “Strings on Orbifolds”, Princeton preprint; E. Witten, “Twistor-Like Transform in Ten Dimensions”, Princeton preprint.
X.G. Wen and E. Witten, “Electric and Magnetic Charges in Superstring Models”, to appear in Nucl. Phys. B.
For a general discussion see E. Witten, “Topological Tools in Ten Dimensional Physics”, and also E. Witten, ref.
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Segre, G.C. (1987). Low Energy Physics from Superstrings. In: Lévy, M., Basdevant, JL., Jacob, M., Speiser, D., Weyers, J., Gastmans, R. (eds) Particle Physics. NATO ASI Series, vol 150. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-1877-4_6
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