In this talk we discuss the need to introduce a string theory in order to obtain a consistent quantum theory of gravity unified with gauge interactions. We then discuss some basic properties of string theory and the origin and the properties of the D(irichlet)-branes. Finally we use them for discussing the Maldacena conjecture and its extension to non-conformal and less supersymmetric theories.
BEYOND THE STANDARD MODELStrong, weak and electromagnetic interactions are described by the standard model that is a gauge field theory based on the group SU (3) c ⊗ SU (2) L ⊗U (1) Y . It has three gauge coupling constants g 1 , g 2 and g 3 and the gauge fields are the 8 gluons, W ± , Z 0 and the photon. It contains two scales: the QCD scale Λ QCD ∼ 250 M eV corresponding to the dimension of a proton that is about 10 −13 cm = 1 F ermi and the Fermi scale ∼ 250 GeV corresponding to the scale at the which the gauge group SU (2) L ⊗ U (1) Y is broken into U (1) em . All present experimental data fully agree with high precision with the predictions of the standard model. As a consequence we can at the moment only speculate on what will happen at higher energy and on which additional scales we could expect. Since the running of the coupling constants g i is entirely predictable from the low-energy particle spectrum and quantum numbers with respect to the gauge groups of the standard model, one can ask oneself if they have the tendency to get together at some higher energy. It turns out that indeed they do at an energy of the order of M GUT = 10 16 GeV and this suggests that the three groups of the standard models may get unified at such a high energy [1]. In addition we know that gravity becomes strong at the Planck mass given by:This means that the standard model, although renormalizable, cannot be a fundamental theory valid at all energies. It is only an effective theory valid at scales << M GUT , M P ℓ . But, if this is the case, then we get the hierarchy problem because we expect a Higgs particle with a mass of the order of the cut-off corresponding in our case to M GUT or M P ℓ , while we need a Higgs particle with a mass of the order of the Fermi scale << M GUT in order to break SU (2) L ⊗ U (1) Y of the standard model in U (1) em . The most popular way out of this problem is to extend the standard model to the minimal supersymmetric standard model where for each particle of the standard model we include also its supersymmetric partners that are required to have a mass of the order of the Fermi scale. Actually it turns out that in this case the three running coupling constants meet all at the same point corresponding to an energy equal to 2 · 10 16 GeV [1]. But also the supersymmetric standard model cannot be a fundamental theory because it does not incorporate quantum gravity and we know that when we reach the Planck mass a classical description of gravity is not anymore consistent. This follows from the fact that a quantum field theory of gravity is not renormalizable. In fact a theory based on pointlike constituents ...
