This talk will consist of three short stories. The first is a standard pep talk and progress report on string theory. For the second and third, I have picked out a pair of recent ideas that may turn out to be important: the existence of a minimum distance in string theory, and string theory as a model for quantum gravity. Let me first mention some general references. Part one is very broad and the reader interested in more detail should start with the textbook by Green, Schwarz, and Witten.' In part two, some specific references are given, but I should mention that 1 picked up this point of view from David Gross. Part three is a summary of my own work.* Extensive references to other work on two-dimensional gravity can be found in that source. The first story starts with our present understanding of fundamental physics, specifically, the quantum field theory known as the Standard Model. This model includes some bosons [the spin-2 graviton, the spin-1 SU(3) x S U ( 2 ) x U(1) gauge bosons, and the spin-0 Higgs boson] and some fermions (the quarks and leptons). The fermions come in 15 kinds (multiplets), in 3 sets (generations) of 5 each. This model is fairly elegant and is consistent with physics over a wide range of energies. In particular, it is consistent with all known physics up to current accelerator energies, as well as with a variety of indirect tests, such as proton decay, a t higher energies. There are many places where non-Standard-Model physics might well have appeared, but there has been no confirmed sign of it. In spite of these impressive successes, the Standard Model cannot be complete. First, it is too arbitrary; it gives no explanation for why these particular particles exist: why is the gauge group SU(3) x SU(2) x U( 1) and why do the fermions come in this precise pattern? In addition, the model involves approximately 20 constants of naturedoupl ings and particle masses-whose values are unexplained. Going further, quantum gravity is probably not a consistent theory due to short distance divergences. These divergences appear to require new physics (although this may not appear until the Planck energy, which is 17 orders of magnitude beyond current accelerator energies). The Standard Model also has some other technical difficulties, known as naturalness problems. Thus, our main guidance in going beyond the Standard Model is the need to explain the pattern of particles and constants and to resolve the divergence and naturalness problems. There are a number of good ideas. One is grand unification, which combines the three gauge interactions into one and the five multiplets in each

Superstring theoryをめぐって(放談室)

Since its proposition over 35 years ago, supersymmetry has been the focus of intense investigation in both theoretical and particle physics. There are many excellent textbooks in the literature which give an introduction to the 'traditional' topics of supersymmetry like the supersymmetry algebra, superfields, supersymmetric gauge theories and supergravity. In recent years our understanding of non-perturbative phenomena in supersymmetric gauge theories has undergone something of a revolution with the use of non-renormalization theorems, duality and holomorphy. These powerful techniques have given new insights into vacuum structure, confinement and strong coupling behaviour of some gauge theories. Non-renormalization theorems in supersymmetric theories have been known for some time. These state that, under some conditions, certain terms of supersymmetric actions are not renormalized in the quantum theory. These include for example the potential term in the Wess–Zumino model and the ultra-violet finiteness of N = 4 supersymmetric gauge theory in four dimensions. The original proof of these theorems was given using light-cone techniques, supergraph methods and anomaly arguments. More recently, non-renormalization theorems have been shown using holomorphy. In many cases, the interaction terms of supersymmetric theories depend holomorphically on chiral superfields and some coupling constants. In addition, these interaction terms are invariant under transformations that act both on the coupling constants and on the fields. Holomorphy is the assertion that after quantum corrections are taken into account, the above interaction terms remain holomorphic in the way suggested above and invariant under the transformations that act on the fields and couplings. This leads to strong restrictions on the type of effective potentials that can occur. In turn, it gives insights into the vacuum structure of gauge theories. Some time ago, it was observed by Montonen and Olive that mass formulae for particle states and magnetic monopoles in gauge theories are invariant under the exchange of particles and magnetic monopoles and the simultaneous inversion of a coupling constant. A consequence of this is that it makes a prediction about the light states of gauge theories at strong coupling. In the last ten years, this paradigm has been extensively investigated and generalized. This book combines the traditional material on supersymmetric gauge theories with the more recent developments on duality and holomorphy. It is the first time that a description of these works on supersymmetry has appeared in book form. The author has made a good selection of topics from a vast literature of research papers and review articles. He has presented the material in a way that leads the reader from the origins to the advanced areas of the field. In particular, the supersymmetric standard model is described. Then holomorphy, Seiberg duality, dynamical supersymmetry breaking and the Seiberg–Witten theory are presented. The book finishes with an outline of the AdS/CFT correspondence. To read the book a good knowledge of quantum field theory and some previous familiarity with supersymmetry are required. The timing for this book could not have been more appropriate. There is much expectation that supersymmetry could be discovered at LHC, CERN. The practitioners of supersymmetry will enjoy reading this book. It will also be an invaluable guide to those who wish to venture onto the landscape of the non-perturbative aspects of supersymmetric gauge theories.

http://iopscience.iop.org/0264-9381/24/2/B01/pdf/0264-9381_24_2_B01.pdf

Modern Supersymmetry, Dynamics and Duality

In this master thesis D-brane-instanton generated contributions to the phenomenology of intersecting D-brane models are investigated. At first a brief introduction to Calabi-Yau and orientifold compactification of supersymmetric string theory is given and the elementary properties and consistency conditions of intersecting brane models like Ramond-Ramond-tadpole cancellation and Green-Schwarz mechanism are explained. The connection between field theoryand D-instantons is shown by the example of the D3/D(-1)-system and the instanton calculus in string theory is described which is the main tool to calculate instanton-contributions to the effective supergravity action. The normalization of the holomorphic contributions in terms of Planckand string-mass is derived. After showing the need for D-brane instantons in the generation of perturbatively forbidden Yukawa couplings in MSSM orientifold models, the implications of the required “Yukawa-instantons” for flavour violating effects are investigated systematically for a specific 5-stack quiver model. Contributions to lepton-flavour violating meson decays are found which are finally used to derive a lower bound on the string mass scale.

/pdf/d-brane-instantons-and-flavour-physics-rez6nkvuce.pdf

D-brane Instantons and Flavour Physics

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D-brane Instantons and Flavour Physics