The Supersymmetric World

The following sections are included:

• FOREWORD
  • References
  • General acknowledgments
  • List of participants

• CONTENTS

My first postdoc started at NAL in September 1969, one of a group of five postdocs, with no senior theorists. NAL, which was to become the Fermi National Accelerator Laboratory, was being energetically built under the guidance of Bob Wilson. In the fall, I was introduced to Professor Nambu by a fellow postdoc and Chicago graduate Lou Clavelli. He was very kind to us, expressing interest in our work on the group-theoretical construction of the dual amplitudes, and even inviting us to lunch at the Quadrangle Club! This was a welcome contrast to visiting theorists who showed little or no interest in our science, with some exception (see later)…

The origins of my involvement in the superstring saga can be traced back to the rather fortuitous and amusing circumstances of my first physical encounter with Pierre Ramond…

Q. To warm up I would like to ask how your early work was related to supersymmetry.

A. The earliest version of string theory (developed in the late 1960's to describe hadron interactions) suffered from various unphysical features. In particular, the spectrum contained a tachyon but no fermions. This motivated the search for a more realistic string theory. The first significant success was made in January 1971 by Pierre Ramond¹ who constructed a string analog of the Dirac equation. At about the same time, Andre Neveu and I were in Princeton constructing a new bosonic string theory. Neveu and I quickly realized² that the two constructions were different facets of a single theory and (along with Charles Thorn) we constructed³ an interacting string theory containing our bosons and Ramond's fermions. In 1972 I showed that consistency of the theory requires that the space-time dimension is 10 and that the ground state fermions are massless…

As is well known, supersymmetry started long before the Iron Curtain was dismantled, and thus came into existence separately in the West and in the former Soviet Union. In order to speak about what I know personally, I will recall that in the West, superalgebras were first considered by A. Neveu, J. Schwarz and P. Ramond as a basic tool to eliminate negative norm states from the spinning string theories. When Neveu, Schwarz and Ramond first introduced them they were initially referred to as supergauges. These authors used the covariant harmonic oscillator approach, the only known technique at the time, without field-theoretic interpretation. Preparing the present text brought back wonderful memories of the time when my long lasting collaboration and friendship with Bunji Sakita^c began. In 1970-71 we started to develop the world–sheet interpretation of the spinning string (unknown at that early time), extending earlier discussions of the purely bosonic case begun by H. Hsue B. Sakita and M. Virasoro¹. We recognized that the Neveu-Schwarz-Ramond (NSR) models included world-sheet two-dimensional Dirac spinor fields, in addition to the world sheet scalar fields, common with the Virasoro model. We showed that the supergauges of the NSR models corresponded to the fact that the two-dimensional world-sheet Lagrangian was invariant under transformations with anticommuting parameters which mixed the scalar and spinor fields. This gave the first example of a supersymmetric local Lagrangian (albeit, two-dimensional)…

In the spring of 1967 I stayed at the ICTP in Trieste for five months. Towards the end of the stay K. C. Wali and I traveled to Israel, specifically the Weizmann Institute for ten days at the invitation of H. J. Lipkin. When we arrived in Israel we found that the atmosphere was extremely tense and people busy preparing for a war with the neighboring Arabic countries. Although the touristy places were deserted, we could manage to rent a car to visit many places including Jerusalem, Haifa and Acre. Since most of the young Israeli physicists had already been drafted, the physicists working at the Institute were mainly foreigners, among whom were H. Rubinstein, G. Veneziano and M. Virasoro. They were working together on superconvergence relations, which was a subject that I was also interested in at that time. In the discussions we had during this visit, the dual resonance program must have come up, since I remember that afterward in Trieste I started discussing with others about the possibility of constructing scattering amplitudes by summing only the s-channel resonance poles. We left Israel as scheduled on June 4 and the very next day in Ankara, Turkey we heard of the outbreak of the Six Day War…

1962: Nine years before the birth of the Superworld in four dimensions. I received a passing grade on my entrance exams to the Department of Physics at Moscow State University but ran into trouble with the medical commission.¹ I gathered my certificates of a winner of many university competitions and arranged an audience with the dean of the School of Physics. I explained to him that I wanted to become a theoretical physicist. His answer was: “No one is above the law”…

Writing this was not easy, for despite the fact that Yuri passed away over five years ago, I still love him. Emotions overwhelm me, making it hard to write something logical. That's why this turned out so chaotic and fragmentary. But I am sending it anyway…

Q. Dmitry Vasilyevich, could you tell me, please, what was your path into theoretical physics, how did you become a theoretician, and was this accidental or was there any specific cause.

A. I was born in Leningrad. When I was 16 years old and when I was studying in the 8th grade, the Great Patriotic War began. I was evacuated from Leningrad. These were very difficult years for young people. In this period I came to work on a collective farm and in a military factory. After that I was drafted into the army and took part as a soldier in the war on the Karelian front, above the polar circle. When the war began with Japan, I participated in military action on the Far Eastern front. I want to say that the war had a considerable influence on my attitude to life. In my generation the war created a feeling of responsibility for the country. After the war we carried over the same ideology into civilian life. When the question of a choice of profession arose, many of us thought about how we might be useful to our country. During all the war years I dreamed about going into science, because already in school I was attracted especially to the exact sciences: mathematics and physics. After the demobilization I entered Leningrad State University, in the faculty of physics. At that time prominent scientists such as V.A. Fock and T.P. Kravets were teaching there. The lectures of T.P. Kravets were distinguished by his ability to link the study material with personal moments. He taught us that physics is created by living people and he spoke much about his teacher Lebedev. From the first days Kravets infected us with a deep love for science, and for physics in particular. Aside from that, I listened to the lectures of V.I. Smirnov, whose widely known multi-volume works were specially intended for theoretical physicists, and, in fact, formed the basis of our whole education. We learned a lot from other mathematicians of his school: O.A. Ladyzhenskaya, M.I. Petrashen. In the final year I received a profound training in the specialization of theoretical physics thanks to the excellent teacher L.E. Gurevich. There were also other teachers, which I remember to this time with thankfulness…

This year the physics community will celebrate the 30-th anniversary of supersymmetry. I want to tell about the first steps in this direction made by our group headed by Professor Dmitri Volkov, in Kharkov…

Thank you for the invitation and your kind introduction. It is a pleasure to be here, and this for many reasons. Let me mention one explicitly. This is the place where Golfand worked during his last years as a member of this faculty and I would like to dedicate this lecture to his memory. As you know, he was one of the founders of supersymmetry…

Recollections on how the basic concepts and ingredients of supergravity were formulated by Dmitri V. Volkov and the present author in 1973-74.

A recollection of some theoretical developments that preceded and followed the first formulation of supergravity theory is presented. Special emphasis is placed on the impact of supergravity on the search for a unified theory of fundamental interactions.

At this point all that comes to my mind is my annoyance at having our note describing the unitary representations rejected by Physical Review Letters as being of “insufficient interest.” I suppose I really suspected that the editor was quite right, and so was annoyed with myself for getting excited about such a far-fetched speculation.

Of course, I now realize, like everyone else, that the subject of supersymmetry is truly interesting …

Having been asked to write some “personal recollections” of the early days of supersymmetry research, I must start with the peculiar apology that they are indeed going to be recollections! Literally. You see, being too young to be writing my memoirs quite yet, I do not have “my papers ordered” to do proper research into my own past. On the other hand, I have been “retired” from academic research for exactly 12 years and 13 days (by the date of the symposium^a) – just long enough not to have names, institutions or, indeed, the latest gossip at my fingertips. As well as to have forgotten a good deal of the physics, and not to be quite sure whether what I do remember was ever correct, or is still considered to be correct. I am sitting here writing in an office of Novell Inc. with lovely high-bandwidth access to the Internet, but no access at all to a library containing Physics Letters or Nuclear Physics B. Sadly, 30-year old high-energy physics papers tend not to be on-line! Which, of course, means that my current “paper” will not have any references, and will mention names only where my middle-aged brain can recall both them and at least a fair approximation of their spelling. It'll all be quite personal…

We recall the obstacles which seemed, long ago, to prevent supersymmetry from possibly being a fundamental symmetry of Nature. Which bosons and fermions could be related? Is spontaneous supersymmetry breaking possible? Where is the spin-½ Goldstone fermion of supersymmetry? Can one define conserved baryon and lepton numbers in such theories, although they systematically involve self-conjugate Majorana fermions? etc. We then recall how an early attempt to relate the photon with a “neutrino” led to the introduction of R-invariance, but that this “neutrino” had to be reinterpreted as a new particle, the photino. This led us to the Supersymmetric Standard Model, involving the SU(3)×SU(2)×U(1) gauge interactions of chiral quark and lepton superfields, and of two doublet Higgs superfields responsible for the electroweak breaking and the generation of quark and lepton masses. The original continuous R-invariance was then abandoned in favor of its discrete version, R-parity – reexpressed as (−1)^2S (−1)^(3B+L) – so that the gravitino and gluinos can acquire masses. We also comment about supersymmetry breaking.

My first encounter with supersymmetry was at the Warsaw conference on mathematics and physics in March 1974, the forerunner of the present-day M∩P conferences. The initial preprint of Wess and Zumino¹ had just appeared and was a subject of informal discussion. Arthur Jaffe, who immediately saw the potential of the idea, and was organizing the field theory section of the 1974 Aspen summer school, invited me to come to the school and lecture on the subject, on the assumption that by June I would be familiar with it. In this way I was precipitated into learning supersymmetry—and fast. In fact, although I immediately embarked on a study of supersymmetry from the few papers available, there was still much to learn when I arrived in Aspen. There I was overawed to find that not only was there a large and distinguished audience of axiomatic field theorists, but also large and distinguished audiences of string theorists and particle physicists eager to learn about this exotic new subject. I had to work extremely hard to prepare the lectures and I recall staying up an entire night at the Institute in preparation for one particular lecture…

I would first like to thank Misha Shifman for his kind invitation to write an article on the paper of Ref. 1 which had the above title. This paper proved that if supersymmetry is preserved at the classical level then the effective potential in a supersymmetric theory had no perturbative quantum corrections. As the paper pointed out, this meant that the degeneracies that were generic in the classical potentials of supersymmetric theories were not removed by perturbative quantum corrections; in modern language supersymmetric theories had moduli. This result, together with earlier work, provided the theoretical basis for the realization that supersymmetry solved the technical hierarchy problem.² In other words, the scalar masses in supersymmetric grand unified theories did not receive large corrections and as a result in supersymmetric theories, once one set a small scale for electro-weak breaking, quantum corrections did not lead to corrections of order the grand unified scale. It also meant that supersymmetry could not be broken by perturbative quantum corrections if it was not broken at the classical level and as a result it placed considerable constraints on the way realistic supersymmetric models could be constructed…

A brief history of ideas which paved the way to supersymmetry is presented.

A short history of the conceptual development that led to the notion of supersymmetry is presented, and some of the developments that arose from the growing understanding of supersymmetry are sketched. Particular emphasis is placed on the role that both ideas about symmetry and symmetry breaking (this latter particularly in the Soviet Union), and ideas born of hadronic string theories (particularly in the West) played in pointing the way to supersymmetry. The related role that supersymmetry later played in reviving interest in string theories is also discussed. Although this brief account is necessarily somewhat narrowly focused, an attempt is made to view these developments from a long-term perspective. A study of the history of supersymmetry provides an ideal opportunity to obtain such a view, because supersymmetry has been at the center of intense interest during a time when both the theoretical and experimental study of high energy physics have changed in significant ways.

The following sections are included:

• EPILOGUE