The Oskar Klein Memorial Lectures

The following sections are included:

• Preface

• CONTENTS

The following sections are included:

• CLASSICAL PERIOD (β DECAY)

• CLASSICAL PERIOD (OTHER WEAK INTERACTIONS)

• TRANSITION PERIOD (1949-1956)

• NEW HORIZON IN THE TRANSITION PERIOD

• THE BREAKTHROUGH (1956)

• SYMMETRY VIOLATIONS

• TIME REVERSAL

• PRESENT STATUS

• PHYSICAL VACUUM

• PHASE DIAGRAM OF THE QCD VACUUM

• ππ-INTERFEROMETRY

• CONCLUDING REMARKS

• REFERENCES

The following sections are included:

• Introduction

• Icosahedral Group

• C₆₀

• Pairing Mechanism

• K₃ C₆₀

• References

The following sections are included:

• Introduction

• Duality in electrodynamics
  • The Coulomb phase
  • The Higgs phase

• The Dynamics of Supersymmetric Field Theories

• Results – duality in non-Abelian theories
  • SU(N_c) with
  • SO(N_c) with N_f × N_c

• Conclusions

• Acknowledgments

• References

This article, based on the Klein lecture, contains some new results and new speculations on various topics. They include discussion of open strings in the AdS space, unusual features of D-branes, conformal gauge theories in higher dimensions. We also comment on the infrared screening of the cosmological constant and on the ”brane worlds”

Recent observational advances have considerably improved the cosmological tests, adding to the lines of evidence, and showing that some issues under discussion just a few years ago may now be considered resolved or irrelevant. Other issues remain, however, and await resolution before the great program of testing the relativistic Friedmann-Lemaître model, that commenced in the 1930s, may at last be considered complete.

The correspondence between supergravity (and string theory) on AdS space and boundary conformal field theory relates the thermodynamics of super Yang-Mills theory in four dimensions to the thermodynamics of Schwarzschild black holes in Anti-de Sitter space. In this description, quantum phenomena such as the spontaneous breaking of the center of the gauge group, magnetic confinement, and the mass gap are coded in classical geometry. The correspondence makes it manifest that the entropy of a very large AdS Schwarzschild black hole must scale “holographically” with the volume of its horizon. By similar methods, one can also make a speculative proposal for the description of large N gauge theories in four dimensions without supersymmetry.

Physicists investigating space, time and matter at the Planck scale will probably have to work with much less guidance from experimental input than has ever happened before in the history of Physics. This may imply that we should insist on much higher demands of logical and mathematical rigour than before. Working with long chains of arguments linking theories to experiment, we must be able to rely on logical precision when and where experimental checks cannot be provided.