From the beginning it was clear that, despite its successes, the Standard Model of elementary particles would have to be embedded in a broader theory that would incorporate gravitation as well as the strong and electroweak interactions. There is at present only one plausible candidate for such a theory: it is the theory of strings, which started in the 1960s as a not-very-successful model of hadrons, and only later emerged as a possible theory of all forces.

There is no one better equipped to introduce the reader to string theory than Joseph Polchinski. This is in part because he has played a significant role in the development of this theory. To mention just one recent example: he discovered the possibility of a new sort of extended object, the ‘Dirichlet brane’, which has been an essential ingredient in the exciting progress of the last few years in uncovering the relation between what had been thought to be different string theories.

Of equal importance, Polchinski has a rare talent for seeing what is of physical significance in a complicated mathematical formalism, and explaining it to others. In looking over the proofs of this book, I was reminded of the many times while Polchinski was a member of the Theory Group of the University of Texas at Austin, when I had the benefit of his patient, clear explanations of points that had puzzled me in string theory. I recommend this book to any physicist who wants to master this exciting subject.

In chapter 8 we found that a number of new phenomena, unique to string theory, emerged when the theory was toroidally compactified. Most notable were the T-duality of the closed oriented theory and the appearance of D-branes in the R → 0 limit of the open string theory. These subjects become richer still with the introduction of supersymmetry. We will see that the D-branes are BPS states and carry R–R charges. We will argue that the type I, IIA, and IIB string theories are actually different states in a single theory, which also includes states containing general configurations of D-branes. Whereas previously we considered only parallel D-branes all of the same dimension, we now wish to study more general configurations. We will be concerned with the breaking of supersymmetry, the spectrum and effective action of strings stretched between different D-branes, and scattering and bound states of D-branes. In the present chapter we are still in the realm of string perturbation theory, but many of the results will be used in the next chapter to understand the strongly coupled theory.

T-duality of type II strings

Even in the closed oriented type II theories T-duality has an interesting new effect. Compactify a single coordinate X9 in either type II theory and take the R → 0 limit.

In this chapter we will examine superstring interactions from two complementary points of view. First we study the interactions of the massless degrees of freedom, which are highly constrained by supersymmetry. The first section discusses the tree-level interactions, while the second discusses an important one-loop effect: the anomalies in local spacetime symmetries. We then develop superstring perturbation theory. We introduce superfields and super-Riemann surfaces to give superconformal symmetry a geometric interpretation, and calculate a variety of tree-level and one-loop amplitudes.

Low energy supergravity

The ten-dimensional supersymmetric string theories all have 32 or 16 supersymmetry generators. This high degree of supersymmetry completely determines the low energy action.

Type IIA superstring

We begin by discussing the field theory that has the largest possible spacetime supersymmetry and Poincaré invariance, namely eleven-dimensional supergravity. As explained in the appendix, the upper limit on the dimension arises because nontrivial consistent field theories cannot have massless particles with spins greater than two.

This theory would seem to have no direct connection to superstring theory, which requires ten dimensions. Our immediate interest in it is that, as discussed in section B.5, its supersymmetry algebra is the same as that of the IIA theory. The action of the latter can therefore be obtained by dimensional reduction, toroidal compactification keeping only fields that are independent of the compact directions. For now this is just a trick to take advantage of the high degree of supersymmetry, but in chapter 14 we will see that there is much more going on.

Thus far we have understood string interactions only in terms of perturbation theory — small numbers of strings interacting weakly. We know from quantum field theory that there are many important phenomena, such as quark confinement, the Higgs mechanism, and dynamical symmetry breaking, that arise from having many degrees of freedom and/or strong interactions. These phenomena play an essential role in the physics of the Standard Model. If one did not understand them, one would conclude that the Standard Model incorrectly predicts that the weak and strong interactions are both long-ranged like electromagnetism; this is the famous criticism of Yang–Mills theory by Wolfgang Pauli.

Of course string theory contains quantum field theory, so all of these phenomena occur in string theory as well. In addition, it likely has new nonperturbative phenomena of its own, which must be understood before we can connect it with nature. Perhaps even more seriously, the perturbation series does not even define the theory. It is at best asymptotic, not convergent, and so gives the correct qualitative and quantitative behavior at sufficiently small coupling but becomes useless as the coupling grows.

In quantum field theory we have other tools. One can define the theory (at least in the absence of gravity) by means of a nonperturbative lattice cutoff on the path integral. There are a variety of numerical methods and analytic approximations available, as well as exactly solvable models in low dimensions. The situation in string theory was, until recently, much more limited.

In the past few years, new methods based on supersymmetry have revolutionized the understanding both of quantum field theory and of string theory.

When I first decided to write a book on string theory, more than ten years ago, my memories of my student years were much more vivid than they are today. Still, I remember that one of the greatest pleasures was finding a text that made a difficult subject accessible, and I hoped to provide the same for string theory.

Thus, my first purpose was to give a coherent introduction to string theory, based on the Polyakov path integral and conformal field theory. No previous knowledge of string theory is assumed. I do assume that the reader is familiar with the central ideas of general relativity, such as metrics and curvature, and with the ideas of quantum field theory through non-Abelian gauge symmetry. Originally a full course of quantum field theory was assumed as a prerequisite, but it became clear that many students were eager to learn string theory as soon as possible, and that others had taken courses on quantum field theory that did not emphasize the tools needed for string theory. I have therefore tried to give a self-contained introduction to those tools.

A second purpose was to show how some of the simplest four-dimensional string theories connect with previous ideas for unifying the Standard Model, and to collect general results on the physics of four-dimensional string theories as derived from world-sheet and spacetime symmetries. New developments have led to a third goal, which is to introduce the recent discoveries concerning string duality, M-theory, D-branes, and black hole entropy.

In this chapter we will consider the notion of partons, in the way Feynman introduced them. The parton model (PM) corresponds to a very clever application of the concepts behind the method of virtual quanta, which we described in Chapter 2. The theoretical reasons why the PM provides a relevant description of the hadronic constituents are, however, very complicated and this chapter only contains a first introduction.

The road to the PM goes through experiment. Over many years physicists have performed in various contexts a type of experiment which can be traced back to Rutherford. They have used a charged particle to extract information on the charge and mass structure of smaller and smaller constituents of matter. Rutherford made use of α-radiation on nuclear targets and very quickly made two essential observations.

He and his assistant were able to detect the scattering of the α-particles by direct observation of the flashes that they produced on a screen. They found, firstly, that most of the beam particles simply continued through the target as if it was empty of matter. But, secondly, every now and then they found quite an appreciable deviation.

It was Rutherford's genius that not only he did take his observations seriously but also used them to provide a description of the atom. We are going to consider his result, together with the necessary corrections due to relativity, spin and the internal structure of the target.

This book stems from lectures in different places and at different times. I would like to thank all those colleagues, graduate students and collaborators, who have patiently listened, commented upon and by insistent questioning given me insight into the physics described in this text.

You will find that the physics is described in a semi-classical language. I believe that my generation, the grandchildren of the wonderful generation that developed the tools of quantum mechanics, have largely learned to use semi-classical dynamical pictures while avoiding the quantum mechanical pitfalls. After having understood that the state density is different and that probabilities are not additive in quantum mechanics most of one's classical intuition can be used. I provide an example in Chapter 2 which shows that you can never fool Heisenberg's indeterminacy relations (i.e. position and conjugate momentum cannot be determined simultaneously with arbitrary precision). But you may choose your variables in such a way (rapidity and position for high-energy particles) that all the quantum mechanical rules are fulfilled and you may still transfer easily between the descriptions in terms of the different variable sets.

The material in the book has been chosen to stress the connections between different approaches to high-energy physics. The basic picture is nevertheless the one stemming from field theory as it is used in the Lund model.

Introduction

In this chapter we consider two different observables, which, within the Lund model, have some bearing upon the confinement properties of QCD.

We start with the Hanbury-Brown-Twiss effect (the HBT effect) or, as it is also called, the Bose-Einstein effect. It originated in astronomical investigations, where one uses the interference pattern of the photons to learn about the size of the photon emission region, i.e. the size of the particular star which is emitting the light.

The Goldhabers, found and used in the same way as HBT a correlation pattern among the produced pions when they investigated proton-antiproton annihilation reactions close to the threshold (i.e. when the annihilation occurs at very low relative velocities, so that the total energy is essentially twice the proton rest mass). Photons and pions have in common that they are bosons, which means that they thrive on being in the same state. The HBT effect can be described as an enhancement of the two-particle correlation function that occurs when the two particles are identical bosons and have very similar values of their energy-momentum.

The size of the emission region obtained from these experiments in hadronic physics seems to be essentially the same in almost any kind of interaction. One obtains a radius of the order of 1 fm, which is a very reasonable size.

Introduction

In this chapter we are going to consider a few further phenomena that should be included in a realistic model for hadron production.

We start by considering heavy flavor fragmentation. There should be no production of heavy flavors in the fragmentation process itself because of the very strong suppression from the tunnelling process. Heavy quark jets will nevertheless occur when the heavy flavor is produced in a process where there is a large energy concentration, e.g. in an e+e– annihilation process. Then the first-rank hadron in the jet contains the heavy flavor and such a hadron will, in general, have a larger mass than the ordinary hadrons, which are made up from the lighter quark flavors, u, d and s. We have seen (cf. Chapter 9) that for the usual Lund fragmentation function a larger-mass hadron will have a ‘harder’ z-spectrum, i.e. the typical value of the fragmentation variable z will be closer to unity.

We will consider a number of different models, both those that tend to give 1 – z ∝ 1/M and those that give 1 – z ∝ 1/M2 for the first-rank hadron with large mass M. We will also consider a rather different treatment which leads to the so-called Peterson formula, for heavy quark fragmentation. The basic idea is to make use of the wave functions obtained in a lightcone-dynamical scenario.

Introduction

In this chapter we will consider some major problems in quantum field theory. They are related to the understanding of polarisation effects in the vacuum state. Although this state in the mean is empty it nevertheless embraces the continuous production and annihilation of virtual particle-antiparticle pairs due to quantum fluctuations. All the real charges and currents then behave as if they were moving in a dielectric medium. In connection with QED this effect is small (although readily observable). For QCD, on the other hand, it plays a major role.

The first kind of problem is mathematical, related to ill-defined series expansions in perturbation theory and also to undefined integrals. The second is general in physics: it is necessary to isolate the effective dependence on the theoretical parameters in all the calculated expressions for the observables (note that this dependence is in general complicated when one deals with non-linear equations). This is the renormalisation procedure, which always must be performed in order to relate the parameters in a theoretical expression to the observables in an experiment.

It is true that physicists are, compared to most other scientists, privileged because the components of many systems in physics can be isolated. In this situation the properties of each component can be determined. Afterwards the whole system can be brought back into interaction, with well-defined values of the parameters which govern the behaviour of each subsystem.