Introduction

In this Chapter we review the developments of string theory from its renaissance in 1984 up to present times, as a kind of epilogue. We shall be rather brief and omit references to original work that would be unavoidably limited: extensive bibliographies can be found in the textbooks mentioned at the end.

After the mid-Eighties, research in string theory was at the forefront in theoretical physics and had a strong impact in many other domains. Even though its main goal, that of unifying fundamental interactions, has not been accomplished yet, and the chances of success are being debated, we can fairly say that string theory has had a broad and lasting influence on theoretical physics. In short, it changed the way research is done in the field. Over the last 25 years, theoreticians were more keen on using advanced mathematical tools and on resorting to abstract modelling: for example, by playing with the spacetime dimension, i.e. considering a given problem also in dimensions different than four. After being presented in the mid-Eighties as ‘the theory of everything’, i.e. of all fundamental interactions, string theory was later dubbed ‘the theory of nothing’ by its opponents; in recent times, it has also been called ‘the theory for everything’, for its many, often unexpected applications.

New techniques of two-dimensional conformal field theory introduced in string theory were employed to describe low-dimensional condensed matter systems and statistical models.

1968. We were young. Revolution was in the air. Gabriele Veneziano's paper [Ven68] was an event in that eventful year. It was immediately clear that it was an important result, but very few people would have thought of it as the beginning of an entirely new theoretical approach that was going to grow in the shell of the old one. It seems appropriate to me to try to combine in this Chapter my personal recollections of the days of the birth of string theory with a few observations on a change in perspective that occurred in theoretical physics. It is a change that we expected in society and that we have witnessed in the course of the years in physics.

It is enough to look at the high energy physics titles of the W. A. Benjamin series Frontiers in Physics, that started in 1961, to get the feeling of the early Sixties: in the first year, Geoffrey F. Chew's S-Matrix Theory of Strong Interactions; in 1963, Regge Poles and S-Matrix by S. C. Frautschi, Mandelstam Theory and Regge Poles by R. Omnès and M. Froissart, together with Complex Angular Momenta and Particle Physics by E. J. Squires; in 1964, Strong-Interaction Physics by M. Jacob and G. F. Chew. Chew's Analytic S-Matrix, with its openly programmatic subtitle A Basis for Nuclear Democracy, was published in 1966, again by Benjamin. In order to complete the list one has to add to these S-matrix inspired titles only a few books, among which is The Eightfold Way by M. Gell-Mann and Y. Ne'eman.

In this Chapter, I recall the sequence of ideas which led to noncritical strings and gauge/strings duality. I also comment on some promising future directions.

In the Sixties I was not much interested in string theory. The main reason for that was my conviction that the world of elementary particles should allow a field theoretic description and that this description must be closely analogous to the conformal bootstrap of critical phenomena. At the time such views were very far from the mainstream. I remember talking to one outstanding physicist. When I said that boiling water may have something to do with the deep inelastic scattering, I received a very strange look. I shall add in the parenthesis that this was the beginning of a long series of ‘strange looks’ which I keep receiving to this day.

Another reason for the lack of interest was actually a lack of ability. I could not follow the very complicated algebra of the early works on string theory and did not have any secret weapon to struggle with it. On the other hand, the Landau Institute, to which I belonged, was full of the leading experts in condensed matter physics. I remember that in the late Sixties to early Seventies Tolya Larkin and I discussed (many times) whether Abrikosov's vortices could be viewed as elementary particles.

In 1969, I was finishing my PhD in Orsay under the supervision of Michel Gourdin on phenomenological works related to e+e- annihilations. These works allowed me to deepen my knowledge of particle physics as well as to learn how to master difficult calculations. However, I was more attracted by more formal research (which we would like to be able to say was more fundamental!). The theoretical physics laboratory in Orsay was also hit by the explosion of activity which followed the paper of Veneziano, and a group of people began to work on dual models: Bouchiat, Gervais, Nuyts, Amati who was spending a sabbatical in Orsay, as well as younger researchers Neveu, Scherk and Sourlas. My first encounter with dual models was to rebel against this too fashionable growing activity. With Jean Nuyts I asked whether there could be some other example of an s–t dual amplitude with only poles in both channels: we found an example with poles lying on a logarithmic trajectory instead of a linear one [CN71]. However, this amplitude led tomany unsatisfactory physical conclusions and I joined the mainstream.

Factorizing the Pomeron with Jöel Scherk at CERN

In 1970, much work was devoted to the dual multiloop amplitude, in particular by Kaku and Yu [KY70]. Lovelace [Lov70] and Alessandrini [Ale71] showed the relation between these amplitudes and the Neumann function associated with a sphere with handles.

String theory was born under the guise of a dual scattering amplitude in the strong interaction community. I still remember the very young Gabriele Veneziano dropping into my office at CERN in 1968 to show me his beta function as an expression for an s-t dual scattering amplitude with only poles (bound states) in both channels and only Regge pole asymptotic behaviours. It looked to me an amusing mathematical realization of an idea that several groups were pursuing. But, I confess, I did not follow the general enthusiasm met by the function as well as its extentions to more particle amplitudes.

The revelation on the road to Damascus, and my subsequent conversion, came to me through the Fubini–Gordon–Veneziano paper in which dual amplitudes were factorized in terms of a well-defined – albeit infinite – set of operators. This implied an operatorial expression for tree diagrams thus ready to be extended so to produce the loop expansion as usually required by unitarity: a process that converted an expression for scattering amplitudes into a perturbative expansion of a full fledged field theory.

At that time, I was spending a sabbatical at Orsay and it took us little time to compute, with Claude Bouchiat and Jean-Loup Gervais, the first loop dual amplitude – and also to infect with enthusiasm for the new theory two bright students who were at the edge of getting their degrees and sailing to Princeton: André Neveu and Joël Scherk.

Abstract

Marco Ademollo, in his contribution to this Volume, has given a review of early work that led to string theory. I will complement this view of that period and its origin. My main purpose is to go further back in time and put the appearance of string theory work in the context of the evolution of the theory of elementary particles.

Introduction

Just after the end of the second world war, the resounding confirmation of relativistic field theory (more precisely, quantum electrodynamics) took place with Lamb's measurement of the level shifts in hydrogen and Schwinger's calculation of the electron magnetic moment, which differed from the value predicted from Dirac's equation. Renormalization theory with American, European, and Japanese contributions gave remarkable results with accuracies beyond one part in one hundred million.

All of these results were obtained using perturbation theory and though the agreement was remarkable, questions of principle on whether the series are convergent and divergences exist, requiring a modification of the theory, loomed in the discussions.

Soon after, with the discovery of mesons, and later other baryons, besides the proton and neutron, attention concentrated on the strong interactions. Pauli, Wentzel, Tamm, Dancoff, Dyson and others worked on the problem (for a short review, see Salpeter [Sal08]).

The natural thing to do was to write a Lagrangian for mesons and nucleons, and try all possible couplings in perturbation theory. It soon became clear that these calculations did not describe the experimental data.

Introduction

By 1973 two ghost-free dual models had been constructed, the Dual Resonance Model and the Ramond–Neveu–Schwarz model. The structure underlying the DRM was that of a relativistic string described by the Nambu–Goto action, but it was not clear yet which kind of string was underlying the RNS model. These models were not suitable for describing strong interactions because they both had massless particles with spins one and two in their spectra (together with a tachyon). An additional problem was raised by the deep inelastic experiments: probing the structure of protons at short distances, they showed the existence of pointlike particles that could be interpreted as the quarks. As already mentioned, string theory scattering amplitudes were too soft at large momentum transfer to explain these experiments. Therefore many researchers went back to field theory; in particular, quantum chromodynamics (QCD), the non-Abelian gauge theory for quarks and gluons formulated in 1972, was intensively studied in the following years obtaining convincing experimental support.

Although these events implied that dual theories could not correctly describe the hadronic processes, they did not completely put an end to their study. In fact, some of the earlyworkers in this field were so attracted by the consistent and deep structure of these models that they continued to study them, sometimes at the price of putting their careers at risk.

In May 2007 we organized a workshop on the origin and early developments of string theory at the Galileo Galilei Institute for Theoretical Physics in Arcetri (Florence). A fair number of researchers who had contributed to the birth of the theory participated and described, according to their personal recollections, the intriguing way in which the theory developed from hadron phenomenology into an independent field of research. It was the first occasion on which they had all been brought together since the 1975 conference in Durham, which represented the last meeting on string theory as applied to hadronic physics.

The workshop in Arcetri was a success: the atmosphere was enthusiastic and the participants showed genuine pleasure in discussing the lines of thought developed during the years from the late Sixties to the beginning of the Eighties, mutually checking their own reminiscences. This encouraged us to go on with the project we had been thinking of for some time, of an historical account of the early stages of string theory based on the recollections of its main exponents. We were fortunate enough to have on board practically all the physicists who developed the theory. While some of the contributions to this Volume originated from the talks presented at the meeting, most of them have been written expressly for this book.

In starting this project we were motivated by the observation that the history of the beginnings and early phases of string theory is not well accounted for: apart from the original papers, the available literature is rather limited and fragmentary.

When I look back at my involvement in the subject of string theory, what strikes me most is that the process of discoveries appears to me rather erratic in the details of who actually makes such or such discovery and when, depending on sometimes strange coincidences. On the other hand, at the level of published work the evolution of scientific knowledge is generally rather smooth and a posteriori natural. Over the decades, I have witnessed several other examples of coincidences that have been crucial in scientific progress. This Chapter is thus in some sense the opposite of Freeman Dyson's article ‘Missed opportunities’ [Dys72] in which he describes contributions he did not make because such coincidences which in all likelihood should have occurred actually did not occur.

In 1968–1969 I was working with Joël Scherk on our research work for our PhD in Orsay under the guidance of Claude Bouchiat and Philippe Meyer. The subject was electromagnetic and final state interaction corrections to nonleptonic kaon decays. We were classmates in our last year as students at the École Normale and good friends. We enjoyed working together a lot. While we were finishing our thesis work, we became very interested in the explosion of activity which followed the original Veneziano paper [Ven68], together with Claude Bouchiat and Daniele Amati, who was spending a sabbatical year in Orsay.

Introduction

The history of the origins and first developments of string theory, from Veneziano's formulation of his famous scattering amplitude in 1968 to the so-called first string revolution in 1984, provides invaluable material for philosophical reflection. The reasons why this episode in the history of modern physics – one still largely unknown to the philosophy of science community despite its centrality to theoretical physics – represents a particularly interesting case study are several and various in nature. It is the aim of the present Chapter to illustrate some of them.

In general, the story of the construction of a new scientific theory is of evident interest in itself, as a concrete example of how a particular theory has been discovered and developed by a given community and over a certain period of time. On the other hand, case studies taken from the history of science are commonly used, by those philosophers of science who pay attention to actual scientific practice, to provide some evidence for or against given positions on traditional epistemological or methodological issues. In other words, with respect to philosophical ‘theories’ on given aspects of the scientific enterprise, historical case studies are attributed a role analogous to that of the data of experience in scientific theories. These aspects can be of a very general character, such as those regarding the methodology, aim and evaluation of scientific theories; or they can be of a more specific kind, such as the significance of a certain principle, argument or concept.

The birth of string theory took place in the years from 1968 (Veneziano formula) to 1973–1974. At the time I was a young physicist interested in the dynamics of strongly interacting particles. This problem was clearly far from being solved but, due to the everyday increase of ‘elementary particles’ and their ‘strong’ interaction, one thing seemed sure to me: the answer was not to be found in quantum field theory!

From the Goldberger–Treiman relation, mNgA = fπGπNN, one obtained GπNN ∼ 10 for the pion–nucleon coupling constant. So a perturbative expansion for the strong interaction was clearly out of the question. But for me it was more than that.With all its ‘infinities’ popping up everywhere, quantum field theory (QFT) appeared to me not only inadequate but just conceptually ‘wrong’ on the whole, because of the large number of ‘unobservable’ quantities it introduced.

In the spirit of Heisenberg the description of the physical world was to be based only on ‘observables’! Since the only really ‘measurable’ quantities were the cross-sections in scattering processes, Chew's ‘bootstrap’ programme seemed the right conceptual framework and his book S-Matrix Theory of Strong Interactions [Che62] was (not only for me, I believe) the reference text.

Of course the calculation of the full S-matrix appeared too ambitious and the immediate objective was to obtain relations among a set of measurable parameters. In this context, a relevant method to obtain physical information was based on the idea, emphasized especially by Sergio Fubini and others, to use dispersion relations together with current algebra to obtain sum rules involving cross-sections.

Abstract

I discuss the early developments of string theory with respect to its connection with gauge theory and general relativity from my own perspective. The period covered is mainly from 1969 to 1974, during which I became involved in research on dual string models as a graduate student. My thinking towards the recognition of string theory as an extended quantum theory of gravity is described. Some retrospective remarks on my later works related to this subject are also given.

Prologue: an encounter with the dual string model

I entered graduate school at Hokkaido University, Sapporo, in April 1969.Myadvisor, Akira Kanazawa, who was an expert in the dispersion theoretic approach to strong interactions, proposed to have a series of seminars on Regge pole theory. However, the Regge pole theory was somewhat disappointing for me. I felt that it was too formal and phenomenological in its nature. Looking for some more favourable topics, I began studying the quantum field theory of composite particles, which, I thought, might be useful to explain the Regge behaviour from the dynamics of fundamental particles. I read many papers related to this problem, such as those on compositeness criteria, on the definition of the asymptotic field for a composite particle, the Bethe–Salpeter equation, and so on. Although I felt that these subjects themselves were not yet what I really wanted to pursue, I enjoyed learning various different facets of quantum field theory.

Today there is a very noticeable tension between string theory and phenomenology in particle physics. It is interesting to muse over the roots of this situation in the very early days of string theory. In this personal account of a small part of the ancient history I review some developments in the string theory groups at Fermilab and Rutgers University in the early Seventies. The present conflict between string theory and phenomenology of particle physics is probably more easily understandable than that of the early days. At its base today is, if sometimes subterranean, a debate over the relative federal funding that the two areas should properly receive. Among phenomenologists there is the perception that progress in string theory has slowed noticeably while still attracting a disproportionate fraction of students and postdoc positions. On the other side there is the feeling that the killing of the Superconducting Super Collider (SSC) project has led to a pronounced drought in the qualitatively new experimental discoveries that could feed phenomenological work. An exception is the confirmation of neutrino masses with well-measured mass splittings and mixing angles. In the beginning, however, string theory (or dual model theory) was totally devoted to the building of a theory of strong interactions that could deal directly with the large amount of data on hadronic phenomena being accumulated at Brookhaven, CERN, and Serpukhov.

One might, therefore, have expected a long honeymoon between dual model theorists and phenomenologists. This however never materialized.