Abstract

I describe the early developments from the formulation of the theory of the relativistic string to the construction of the first consistent superstring theory, which I witnessed from a very short distance.

The relativistic string

The story begins in October 1972, when in a CERN preprint Goddard, Goldstone, Rebbi and Thorn (GGRT) formulated a complete theory of the quantized free relativistic string [GGRT73] describing the physical states of the Dual Resonance Model.

At that time this model of strong interactions, arisen from the Veneziano amplitude proposed in 1968,was already completely developed. Fubini andVeneziano [FGV69, FV69, FV70] and Bardakci and Mandelstam [BM69] had shown that the single-particle states of the Dual Resonance Model (DRM) could be described consistently by an infinite collection of harmonic oscillators. Nambu, Nielsen and Susskind had formulated independently the conjecture that the underlying microscopic structure of these physical states was a vibrating string. Nambu was apparently the first one to use this term in such a context, writing: ‘This equation suggests that the internal energy of a meson is analogous to that of a quantized string of finite length’ [Nam70a]. Susskind used a funny paraphrase: ‘a continuum limit of a chain of springs’ [Sus69], and in a note added in proof, where the works on the factorization of the N-point amplitude by Fubini and Veneziano and by Bardakci and Mandelstam were explicitly mentioned, he used the term ‘rubber band’.

Abstract

I worked on string theory over a period of five years during the ‘first string era’, the most intellectually satisfying years of my scientific life. One of the early prospectors in the string theory mine, I was fortunate enough to contribute to the birth of this subject, which retains after these many years, its magical hold on our imaginations and expectations.

Graduate school

I was born in Neuilly sur Seine, a suburb of Paris, where I attended Sainte Croix de Neuilly. After the ‘deuxième bachot’ in 1961, I decided to spend a year with my family in New Jersey, where my civil engineer father had been working for a company that designed and manufactured concrete pipes. I enrolled at the Newark College of Engineering (NCE); there, I found spectacular teachers, especially Dr Foster, and one year turned into four; I graduated in 1965 with a Bachelor of Science in electrical engineering.

Always interested in physics, I had studied the subject on my own while at NCE. My application to Princeton graduate school in physics was rejected (and wait-listed at Yale). Fortunately, I had also applied to Syracuse University where Peter Bergmann was teaching. With the recommendations of Professors Henry Zatzkis (a student of Bergmann), Mauro Zambuto, and A. E. Foster, I was accepted, and soon afterwards, awarded a four-year fellowship.

I had wanted to study general relativity with Bergmann, but I was persuaded by Professor Alan McFarlane to switch to particle physics and join the group headed by E. C. G. Sudarshan.

Introduction

My generation of string theorists was very fortunate. We were there when the first ideas leading up to string theory were proposed, and we were young and inexperienced enough not to ask too deep questions. We could accept working in 26 dimensions of spacetime, even when more experienced people laughed at it (and us). We were not more clever than they were, not at all, rather we became so attached to the ideas that we did not listen to good advice. The average age of the active people was probably well under thirty, and it was one of the rare occasions where a young generation could form its scientific future. There were a number of older heroes, most notably Yoichiro Nambu, Stanley Mandelstam, Sergio Fubini and Daniele Amati. Also, the leading theoretical physicist of those days, Murray Gell-Mann, was sympathetic. His words, always carefully phrased, were listened to by everyone in particle physics. This blend made the field so exciting that once hooked it was difficult to leave it. After some years many had to change field in order to find positions, but most of us had the secret wish to return to this subject.

The formative years

I started as a graduate student in 1967. Sweden still had the old system, which meant that there were no graduate schools. You had to study on your own, and you had to work on your own.

Abstract

These are my personal impressions of the environment in which string theory was born, and what the important developments affecting my work were during the hadronic string era, 1968–1974. I discuss my motivations and concerns at the time, particularly in my work on loop amplitudes and on closed strings.

Introduction

It is not unusual in theoretical physics for conceptual frameworks to ride roller-coasters, but few have had as extreme highs and lows as string theory from its beginnings in 1968 to the present. In fact, string theory was so dead in the mid to late Seventies that it is a common assumption of many articles in the popular press, and of many younger string theorists, that the field originated in the Eighties, completely ignoring the period we are discussing here, which is primarily 1968–1974. So it was pleasantly surprising to be invited to reminisce about the early days of string theory. Research results from that era have been extensively presented and reviewed, so I will try to give my impression of the atmosphere at the time, and what questions we were trying to settle, rather than review the actual results.

The placenta

In themid-Sixties, the framework for understanding fundamental physics was very different from what it is now. We still talk about the four fundamental interactions, but we know that the weak and electromagnetic interactions are part of a unified gauge field theory, that strong interactions are also described by a gauge field theory which might quite possibly unify with the others at higher energy, and that even general relativity is a form of gauge field theory.

String theory traces its origin to the Veneziano model of 1968. It also happens that the Weinberg–Salam model was born about the same time. The latter has led to the successful Standard Model. The descendants of the former, on the other hand, are still struggling to be relevant to the real world in spite of their enormous theoretical appeal. Indeed there exist two pathways in the development of theoretical particle physics since its beginnings in the Thirties. I will call them the quantum field theory and the S-matrix theory respectively. In its historical lineage, the Standard Model belongs to the former, whereas the superstring theory belongs to the latter. Even though the former has turned out to be the Royal Road of particle physics, this was not entirely clear before its final triumph, and the latter has also played very important contributing roles which continue to this day. The purpose of this note is to follow this other pathway and discuss the topics that have influenced my thoughts.

In the Thirties, when nuclear physics was developing, there were uncertainties in the minds of physicists about the efficacy of quantum field theory which was still in its early stages of development. For one thing, quantum field theory had inherited the self-energy difficulty from classical theory although the degree of divergence was found to be milder. For another, the unknown nature of nuclear forces and the much higher energy range involved than in atomic phenomena made people suspect that quantum mechanics might fail in dealing with nuclear phenomena, just as the classical theory failed with atomic phenomena.

Introduction

During the Fifties it became clear that quantum electrodynamics (QED), constructed by applying the quantization rules to classical electrodynamics, was in very good agreement with experimental results. In particular, QED accounted for the deviations observed in experiments with respect to the Dirac theory of electrons and positrons. This was considered a major success of field theory.

In the following years, many efforts were made in the attempt to build a suitable theory for the description of the weak and strong interactions of elementary particles. These efforts culminated in the formulation of the electro-weak theory of Weinberg and Salam in 1967, and quantum chromodynamics in 1973. These are the two fundamental blocks of the Standard Model.

In the Sixties, when the theoretical community was still seeking a satisfying theory of strong interactions, several alternative approaches were explored, to overcome the encountered difficulties. In particular, one of these, the S-matrix, complemented with the bootstrap hypothesis and Dolen–Horn–Schmid duality, was to give rise to dual models and string theory.

The aim of the present Chapter is to recall some of the relevant results which originated in this context, in the years between 1961 and 1968, and which led to the Veneziano formula. In the next Section I will sketch the SU(3) symmetry and the quark model. In Section 6.3 I will recall current algebra, with a glance at its exploitation by means of sum rules.

Abstract

This Chapter surveys some of the highlights in the development of string theory through to the first superstring revolution in 1984. The emphasis is on topics in which the author was involved, especially the observation that critical string theories provide consistent quantum theories of gravity and the proposal to use string theory to construct a unified theory of all fundamental particles and forces.

Introduction

I am happy to have this opportunity to reminisce about the origins and development of string theory from 1962 (when I entered graduate school) through to the first superstring revolution in 1984. Some of the topics were discussed previously in three papers that were written for various special events in 2000 [Sch00a, Sch00b, Sch01]. Also, some of this material was reviewed in the 1985 reprint volumes [Sch85], as well as string theory textbooks (Green, Schwarz and Witten [GSW87] and Becker, Becker and Schwarz [BBS07]). In presenting my experiences and impressions of this period, it is inevitable that my own contributions are emphasized.

Some of the other early contributors to string theory present their recollections elsewhere in this Volume. Taken together, these contributions should convey a fairly accurate account of the origins of this remarkable subject. Since the history of science community has shown little interest in string theory, it is important to get this material on the record. There have been popular books about string theory and related topics, which serve a useful purpose, but there remains a need for a more scholarly study of the origins and history of string theory.

Introduction

The connection between the Dual Resonance Model (DRM) and the relativistic string, a one-dimensional extended system, was observed soon after Veneziano's fundamental paper. Indeed, the presence of an infinite set of harmonic oscillators, with frequencies that were multiples of a fundamental tune, was clearly suggestive of a vibrating string.

Part IV contains the contributions by the authors who proposed the string interpretation, found the action and studied the quantization. In the years 1969 and 1970, Nambu, Nielsen and Susskind, each from his own perspective, suggested independently that a string model was at the basis of the DRM. In 1970, Nambu, and later Goto, wrote the correct relativistic and reparameterization-invariant form of the string Lagrangian. The different perspectives can be summarized as follows.

1. (i) Susskind's starting point was the comparison of DRM scattering amplitudes with those for the relativistic harmonic oscillator. From the existence of many frequencies of oscillation, i.e. harmonics, Susskind had the idea of a ‘rubber band’ or a ‘violin string’.

2. (ii) Nielsen's intuition came from an analogy of dual diagrams with high-order Feynman diagrams, called ‘fishnet diagrams’ in this approximation particles interact approximately with nearest neighbours and effectively form a one-dimensional chain, i.e. a string.

3. […]

Abstract

This Chapter gives an overview of my period of research in string theory up to the end of 1984. I will begin with my time as a graduate student and postdoc, which coincided with the earliest developments in dual models and string theory. However, I will not repeat the detailed history of this early period, which is covered much more completely by other authors in this Volume. The second part will concern the development of string theory with manifest spacetime supersymmetry in the late Seventies and early Eighties, a period that postdates most of the other contributions in this Volume.

String theory till 1979

The subject of string theory has its genesis in the many wonderful developments in relativity and quantum theory in the first half of the twentieth century. Two singular results of the early to mid-Sixties are particularly relevant to subsequent developments in string theory. One of these was the formulation by Dirac of a theory of the relativistic membrane [Dir62] (eight years before the formulation of the relativistic string, Nambu and Goto [Nam70, Got71]), in which he attempted to describe the μ-meson as a radial excitation of a spherical membrane whose ground state was the electron. This inspired paper was effectively ignored until the subject of supermembranes became fashionable in the late Eighties. It now plays a key role, in association with Born and Infeld's long-neglected nonlinear electrodynamics [BI34], in the Dirac–Born–Infeld description of D-branes. A second important insight of the mid-Sixties was Hagedorn's implementation of the bootstrap programme.

In this short account Iwould like to think about the remarkable history of the development of relativistic string theories which have gradually renewed the very foundations of theoretical high energy physics. For lack of time and precise knowledge, Iwill stick tomy own personal contribution at the beginning of this wonderful story, and refer to other contributions in this Volume to complete the picture.

The year 1968–1969, marked a turning point in my career, not only because string theory came into the fore. I was just returning from two years as a postdoc at New York University, where I had met J. Wess (a visitor for one year), B. Zumino (then the head of the Theory Group located at the Courant Institute), K. Symanzik, W. Zimmermann and D. Zwanziger. My earlier interests were mostly on dispersion relations, Regge poles, and S-matrix theory, but at NYU, I had been fully converted to local field theory, and much impressed by the power of symmetries in that context, be they local or global, exact or (spontaneously) broken. Of course, this year saw the beginning of string theory, which was however initially developed using the covariant operator method within the context of S-matrix theory, giving what looked like a realization of G. Chew's programme. I refer to the contribution of Ademollo to this Volume for a review of the precursory works which led Veneziano to write his celebrated four-point function.

Introduction

Part II deals with theoretical particle physics in the Sixties and the developments that led to the Veneziano formula for the scattering amplitude of four mesons – the very beginning of string theory. In this Introduction, we provide some background for these developments.

We begin by recalling some aspects of quantum field theory, the basic theory for describing elementary particles and fundamental interactions. Quantum field theory was fully developed during the Fifties and successfully applied to the description of the electromagnetic force, leading to quantum electrodynamics (QED), the theory of photons, electrons and positrons. Remarkably, QED predicted new quantum-relativistic effects, such as the anomalous magnetic moment of electrons and the Lamb shift in atomic spectra, which were confirmed experimentally to very high precision.

A crucial aspect of the theory was the presence of a small parameter, the fine-structure coupling constant α ∼ 1/137: all quantities could be expanded in power series of α, the socalled perturbative expansion, and the first few terms were precise enough to be compared with the experimental data. This approximation allowed the complexity of field interactions to be disentangled.

At the beginning of the Sixties, quantum field theory methods were also applied to the weak nuclear force (responsible for radioactive decays) and the strong force (gluing protons and neutrons inside nuclei), the names clearly indicating their strength. Weak interactions could be described within perturbative quantum field theory, although with the limitations due to the incompleteness of the Fermi theory (see Appendix A for more details).

The year 1968 was quite remarkable also in science: it was the year of the Veneziano formula, a real breakthrough towards new horizons in theoretical physics.

In July 1968 in Turin we heard a seminar by Gabriele Veneziano who came to submit his beta function amplitude to the attention of Sergio Fubini, an opinion leader in the theory of strong interactions after his works on current algebra (the p→∞ method, with G. Furlan) and on superconvergence (with V. De Alfaro, G. Furlan and C. Rossetti). Fubini encouraged Veneziano to publish his paper, which soon appeared [Ven68] in Nuovo Cimento (at that time the most important journal in high energy physics in Europe) and invited the young physicists in Turin to look at this promising model.

Actually my interest increased when the generalization of the Veneziano amplitude to N points was proposed by K. Bardakci, H. Ruegg, M. A. Virasoro, H.M. Chan, S. T. Tsou, C. J. Goebel, B. Sakita, Z. Koba and H. B. Nielsen. I was fascinated by the elegance of the ‘duality rules’: the poles in the various channels were exhibited by simple changes of integration variables, dictated by (elementary) geometry.

My enthusiasm burst in the spring of 1969, when Miguel Virasoro gave a seminar in Turin on his work with Keiji Kikkawa and Bunji Sakita [KSV69]: up to some (crucial) factors, the structure of the multiloop amplitudes was simply dictated by consistency with the duality rules.

Here is how I remember it. Supposedly I was a particle physicist: indeed I had spent three years as a graduate student in Cornell (1962–1965) and a year as a postdoc in Berkeley (1965–1966), learning about S-matrix theory, and hating every minute of it. The general opinion among leaders of the field was that hadronic length and time scales were so small that in principle it made no sense to probe into the guts of a hadronic process – the particles and the reactions were unopenable black boxes. Quantum field theory was out; Unitarity and Analyticity were in. Personally, I so disliked that idea that when I got my first academic job I spent most of my time with my close friend, Yakir Aharonov, on the foundations of quantum mechanics and relativity.

By 1967 I was convinced that the S-matrix black-box view was wrong-headed. I had spent a lot of time formulating relativistic quantum theory in what was then called the infinite-momentum frame (IMF), now called the light-cone frame. The idea that appealed to me was that by boosting a system to very large momentum you could slow down its internal motions. By stationing a sequence of detectors along the direction of the boost, one could imagine probing an interacting system of hadrons as it evolved. I wrote a lot of papers showing among other things that physics in the IMF had a Galilean symmetry so that the ordinary rules of nonrelativistic quantum mechanics must apply.