D-brane Instantons and Flavour Physics

Abstract: 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

TL;DR: In this article, a reasonably connected outline of quantum field theory is given, from second quantization to the path-integral technique in Euclidean space, where there is an immediate connection with the rules for Feynman diagrams and the partition function of Statistical Mechanics.