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Nambu, a Foreteller of Modern Physics
Special Sections of PTEP



Professor Yoichiro Nambu, the Nobel Prize winning theoretical physicist, passed away on July 5, 2015, in Osaka at the age of 94. The legacy of his research in theoretical physics has had a profound impact on generations of researchers around the world. To honor his great achievements, Progress of Theoretical and Experimental Physics (PTEP) has published a series of special sections featuring invited articles dedicated to Professor Yoichiro Nambu. This article introduces the background and the content of these special sections, which contain a number of innovative scientific results and fascinating stories associated with Professor Nambu.

Nambu in Japan and in US

Yoichiro Nambu was born on January 18, 1921, in Tokyo, Japan. He graduated from then Fukui Secondary High School in Fukui City and was enrolled at the Imperial University of Tokyo. He developed his interest in physics as a collegiate student, and was intellectually stimulated by Hideki Yukawa, a leading particle theorist at the time. He received his Bachelor of Science in 1942 from the University of Tokyo, before being drafted into the Japanese army and assigned to work in the radar laboratory led by Shin-ichiro Tomonaga, another leading particle theorist of his day. In 1950, at the age of 29, he became an associate professor at the newly created Osaka City University in Japan. He received his Doctor of Science degree in 1952 from the University of Tokyo. In this post-war period, the overall social conditions in Japan were still poor and turbulent, but his group nevertheless enjoyed an open and active atmosphere in which to carry out their research, and produced a number of achievements as a result.


Fig. 1: Yoichiro Nambu from Progress of Theoretical Physics Supplement, 86 (1986).

Nambu retained his post at Osaka City University until 1956, but moved to the US in 1952 to work at the Institute for Advanced Study in Princeton, N.J.. This was at the invitation of J. Robert Oppenheimer and thanks to the recommendation of Tomonaga. It has since become a famous anecdote that Nambu mustered enough courage to have a rare and enjoyable encounter with the legendary figure, Albert Einstein at Princeton. In 1954, Nambu moved to the University of Chicago, and became an associate professor in 1956 and a professor in 1958. He obtained U.S. citizenship in 1970. He was named the Harry Pratt Judson Distinguished Service Professor in 1977, and retired as a professor emeritus at the University of Chicago's Department of Physics and Enrico Fermi Institute in 1991. In later years, he also served as a distinguished professor at the University of Osaka in Japan and often stayed at his home in Osaka as well as in Chicago.

Nambu and Modern Physics

Among Nambu's numerous important contributions in physics, three are worthy of special mention. First, in collaboration with Moo-Young Han, Nambu proposed the "color charge" of quantum chromodynamics. This was the forerunner of the modern theory of quantum chromodynamics, which accounts for the nuclear forces that bind protons and neutrons into atomic nuclei. Second, Nambu discovered the phenomenon of spontaneous symmetry breaking in particle physics. Stimulated by the BCS theory of superconductivity, he studied superconductivity intensely, and then applied the concept of spontaneous symmetry breaking to chiral symmetry in two influential papers with Giovanni Jona-Lasinio. Massless bosons arising in field theories with spontaneous breaking of continuous global symmetry are referred to as Nambu-Goldstone bosons. Third, he discovered that the dual resonance model can be explained as a quantum mechanical theory of strings. The Nambu-Goto action in string theory is named after Nambu and Tetsuo Goto. Nambu is considered to be one of the founders of string theory.

Nambu's profound insight led to a vast array of scientific endeavors that still continue today, even half a century after his original papers were published. In essence, Nambu laid the foundations of modern physics and set the direction of research for decades to come. We can truly describe him as a foreteller of modern physics.

Nambu obtained many honors and awards, including the Dannie Heineman Prize in 1970, the J. Robert Oppenheimer Memorial Prize in 1977, the Order of Culture from the Japanese government in 1978, the National Medal of Science of the United States in 1982, the Max Planck Medal in 1985, the Dirac Prize in 1986, the Sakurai Prize in 1994, the Wolf Prize in Physics in 1994/1995, the Franklin Institute's Benjamin Franklin Medal in 2005, and the Pomeranchuk Prize in 2007. He was awarded the 2008 Nobel Prize in Physics, jointly with Makoto Kobayashi of the High Energy Accelerator Research Organization (KEK) in Tsukuba, Japan, and Toshihide Maskawa of Kyoto University in Japan, "for the discovery of the mechanism of spontaneous broken symmetry in subatomic physics". His many honors included membership in the National Academy of Sciences, honorary membership in the Japan Academy, and in the Physical Society of Japan. He also was a fellow of the American Academy of Arts and Sciences.

Nambu inspired many researchers around the world with his groundbreaking scientific achievements and through his helpful advice. Nambu made contributions in numerous aspects of science and has had a tremendous influence on researchers world-wide. With his passing, many felt that they had lost one of the giants of 20th-century theoretical physics. Researchers around the world felt a particularly deep sorrow with the loss of Professor Nambu, and have held a series of three symposia in his honor.

Some of Nambu's works have been published in Progress of Theoretical Physics, and they continue to have a strong impact on the scientific community to this day. As a member of the advisory board of Progress of Theoretical and Experimental Physics (PTEP), Nambu, with his warm personality, also guided PTEP in its initial years of publication. On this occasion, PTEP has decided to publish a series of special sections dedicated to Professor Nambu, consisting of invited articles contributed by the speakers at the three symposia.

Special Section I: Osaka City University Symposium

The first of these symposia was held on September 29, 2015 and was entitled, "Great Achievements of Professor Nambu to be Learned by Students and Researchers" at Osaka City University, Osaka, Japan. Osaka City University was the starting place of Nambu's professional career. Before his departure to the United States, he led a newly created theoretical physics group at Osaka, which had a number of active researchers: Sachio Hayakawa, Yoshio Yamaguchi, Kazuhiko Nishijima, and Tadao Nakano. Much later, he paid a number of visits to Osaka City University while he was staying in Osaka in order to encourage young students based there.

There were a variety of talks at the symposium, which reflected the versatility and profundity of Nambu's research achievements, and the talks were of great benefit to the diverse audience representing a wide spectrum of the scientific community. The special section dedicated to Professor Nambu in the June 2016 issue of PTEP is a collection of invited articles contributed by speakers at the symposium held at Osaka City University.

Kazuo Fujikawa introduced the modern significance of the works of Nambu and Jona-Lasinio. Nobuhito Maru described the dynamical breaking of supersymmetry, which occurs nonperturbatively in a similar way to Nambu's idea. Hiroshi Itoyama gave a historic account of the development of string theory and the deep influence provided by Nambu. Yutaka Matsuo explained the role played by the Nambu bracket in string theory. Sanefumi Moriyama and his collaborators proposed a new formulation of M2 branes in terms of the Nambu bracket. Yukinori Sakuragi discussed nuclear forces and the equation of state inside neutron stars. Koichi Yamawaki discussed the status of composite models for the Higgs particle.

• "BCS, Nambu-Jona-Lasinio, and Han-Nambu: A sketch of Nambu's works in 1960-1965"
    Kazuo Fujikawa, Prog. Theor. Exp. Phys. 2016, 06A101 (2016). doi:10.1093/ptep/ptw029
• "Nambu-Jona-Lasinio theory and dynamical breaking of supersymmetry"
    Nobuhito Maru, Prog. Theor. Exp. Phys. 2016, 06A102 (2016). doi:10.1093/ptep/ptw018
• "Birth of string theory"
    Hiroshi Itoyama, Prog. Theor. Exp. Phys. 2016, 06A103 (2016). doi:10.1093/ptep/ptw063
• "Nambu bracket and M-theory"
    Pei-Ming Ho and Yutaka Matsuo, Prog. Theor. Exp. Phys. 2016, 06A104 (2016). doi:10.1093/ptep/ptw075
• "Prospect of the Nambu bracket"
    Kazuki Kiyoshige, Sanefumi Moriyama, and Katsuya Yano, Prog. Theor. Exp. Phys. 2016, 06A105 (2016).
• "Saturation of nuclear matter and roles of many-body forces: nuclear matter in neutron stars probed
    by nucleus-nucleus scattering"
    Yukinori Sakuragi, Prog. Theor. Exp. Phys. 2016, 06A106 (2016). doi:10.1093/ptep/ptw072
• "The origin of mass: horizons expanding from Nambu's theory"
    Koichi Yamawaki, Prog. Theor. Exp. Phys. 2016, 06A107 (2016). doi:10.1093/ptep/ptw077


Fig. 2: Hiroshi Itoyama presenting a lecture at the Nambu symposium at Osaka City University.

Special Section II: Osaka University Symposium

The second of these symposia was entitled, "Nambu's Century: International Symposium on Yoichiro Nambu's Physics", and was held on November 16, 2015 at Osaka University. Nambu visited Osaka University regularly when he stayed in Japan, especially during his final years. He had many inspiring discussions with scientists there and his generous and humane personality left a lasting impression.

Numerous prominent scientists came or sent heart-warming messages, reflecting the long friendships Nambu held with many distinguished international figures. The symposium was attended by an audience representing a broad spectrum of the scientific community and they enjoyed a variety of engaging talks. The special section dedicated to Professor Nambu is a collection of invited articles contributed by the speakers at the symposium held at Osaka University.

Steven Weinberg pointed out that the concept of spontaneous symmetry breaking proposed by Nambu decided the course of subsequent physics research. Makoto Kobayashi noted that our understanding of CP violation in the Standard Model is related to Nambu's work on the spontaneous breaking of chiral symmetry. Giovanni Jona-Lasinio gave an historical account of the Nambu-Jona-Lasinio theory. Motohiko Yoshimura described the possibility of detecting lepton-number violation in neutrino processes via the macro-coherent mechanism. Lars Brink described Nambu's broad and deep influence. Pierre Ramond gave a new formulation of (2,0) superstring. Peter Freund provided historical perspective regarding Nambu's achievements after his arrival in the United States. Toichiro Kinoshita described the scientific climate in post-war Japan and Nambu's influence.

• "Nambu, at the beginning"
    Steven Weinberg, Prog. Theor. Exp. Phys. 2016, 07B002 (2016). doi:10.1093/ptep/ptv186
• "Personal recollections on chiral symmetry breaking"
    Makoto Kobayashi, Prog. Theor. Exp. Phys. 2016, 07B101 (2016). doi:10.1093/ptep/ptw021
• "Yoichiro Nambu: remembering an unusual physicist, a mentor and a friend"
    Giovanni Jona-Lasinio, Prog. Theor. Exp. Phys. 2016, 07B102 (2016). doi:10.1093/ptep/ptw028
• "Yet another symmetry breaking to be discovered"
    Motohiko Yoshimura, Prog. Theor. Exp. Phys. 2016, 07B103 (2016). doi:10.1093/ptep/ptw056
• "Some reminiscences from a long friendship"
    Lars Brink, Prog. Theor. Exp. Phys. 2016, 07B104 (2016). doi:10.1093/ptep/ptw044
• "Travels with Nambu"
    Pierre Ramond, Prog. Theor. Exp. Phys. 2016, 07B105 (2016). doi:10.1093/ptep/ptw048
• "Nambu at work"
    Peter G. O. Freund, Prog. Theor. Exp. Phys. 2016, 07B106 (2016). doi:10.1093/ptep/ptw054
• "Personal Recollection, 1945 - 1960"
    Toichiro Kinoshita, Prog. Theor. Exp. Phys. 2016, 07B107 (2016). doi:10.1093/ptep/ptw064


Fig. 3: Makoto Kobayashi speaking at a lecture at the Nambu symposium in Osaka University.


Fig. 4: Participants of the Nambu symposium at Osaka University.

Special Section III: Chicago University Symposium

The third of these symposia was entitled "Nambu Memorial Symposium", and was held on March 11 - 13, 2016 at the University of Chicago in the United States.

The University of Chicago was Nambu's home institution for nearly forty years. During that time, he played a pivotal role in physics research and made a tremendous impact on the people around him and people around the world, leaving behind the lasting impression of his quiet, warm personality, as well as his profound scientific insight.

The symposium was held to celebrate the life and scientific achievements of Yoichiro Nambu. Numerous prominent international scientists travelled to Chicago to give lectures on innovative research in the broad array of research areas in which Nambu made seminal contributions: particle physics, condensed matter physics, quantum field theory, and string theory.

This special section dedicated to Professor Nambu is a collection of invited articles contributed by the speakers at the symposium held at the University of Chicago.

Nathan Seiberg gave a brilliant account of topological insulators in collaboration with Edward Witten. Subir Sachdev and his collaborator described their new theory of topological Fermi liquids. Dam Tranh Son explained the fractional quantum Hall effect using the theory of Dirac composite fermions. Juan Maldacena and his collaborators worked out conformal symmetry breaking in nearly AdS space in 2 dimensions. Igor R. Klebanov and his collaborators gave an account of Yukawa conformal symmetry and emergent supersymmetry. Michael Dine described the role of Nambu-Goldstone and other light particles in cosmology. Sumit R. Das gave a summary of various scaling laws in quantum quench. Hirosi Ooguri presented a gravitational positive energy theorem. Tohru Eguchi gave a brief account of the moonshine phenomena in string theory. Greg Moore described BPS states in N=2 supersymmetric theories.

• "Gapped boundary phases of topological insulators via weak coupling"
    Nathan Seiberg and Edward Witten, Prog. Theor. Exp. Phys. 2016, 12C101 (2016). doi:10.1093/ptep/ptw083
• "The novel metallic states of the cuprates: Topological Fermi liquids and strange metals"
    Subir Sachdev and Debanjan Chowdhury, Prog. Theor. Exp. Phys. 2016, 12C102 (2016). doi:10.1093/ptep/ptw110
• "The Dirac composite fermion of the fractional quantum Hall effect"
    Dam Thanh Son, Prog. Theor. Exp. Phys. 2016, 12C103 (2016). doi:10.1093/ptep/ptw133
• "Conformal symmetry and its breaking in two dimensional Nearly Anti-de-Sitter space"
    Juan Maldacena, Douglas Stanford, and Zhenbin Yang, Prog. Theor. Exp. Phys. 2016, 12C104 (2016).
• "Yukawa CFTs and emergent supersymmetry"
    Lin Fei, Simone Giombi, Igor R. Klebanov, and Grigory Tarnopolsky, Prog. Theor. Exp. Phys. 2016, 12C105 (2016).
• "Light scalars and the cosmos: Nambu-Goldstone and otherwise"
    Michael Dine, Prog. Theor. Exp. Phys. 2016, 12C106 (2016). doi:10.1093/ptep/ptw141
• "Old and new scaling laws in quantum quench",
    Sumit R. Das, Prog. Theor. Exp. Phys. 2016, 12C107 (2016). doi:10.1093/ptep/ptw146
• "Gravitational positive energy theorems from information inequalities"
    Nima Lashkari, Jennifer Lin, Hirosi Ooguri, Bogdan Stoica, and Mark Van Raamsdonk, Prog. Theor. Exp. Phys. 2016,
    12C108 (2016). doi:10.1093/ptep/ptw139
• "Professor Nambu, string theory and moonshine phenomenon"
    Tohru Eguchi, Prog. Theor. Exp. Phys. 2016, 12C109 (2016). doi:10.1093/ptep/ptw132
• "A note on the semiclassical formulation Of BPS states in four-dimensional N=2 theories"
    T. Daniel Brennan and Gregory W. Moore, Prog. Theor. Exp. Phys. 2016, 12C110 (2016). doi:10.1093/ptep/ptw159


Norisuke Sakai is the editor in chief of Progress of Theoretical and Experimental Physics, and a visiting professor at the Research and Education Center for Natural Sciences, Keio University. After receiving a D. Sci. from the University of Tokyo, he worked at the Max-Planck Institute of Physics, Rutherford Laboratory, Tohoku University, Nordita, Fermilab, KEK, Tokyo Institute of Technology, and Tokyo Woman's Christian University before joining Keio University in 2014. His research field is theoretical particle physics.