Keiji Kikkawa

We regret to report the passing of Keiji Kikkawa of Osaka University on July 1, 2013, who helped to lay the foundation of string/M theory. The theory has gone through many tortuous stages, and remarkably, he was able to make crucial breakthroughs in all of them.

Kikkawa was born on Oct. 1, 1935 in Shimane Prefecture, Japan. He received his bachelor’s degree from Tokyo Metropolitan University in 1959, went on to get his doctorate from the University of Tokyo in 1964, and then went to the United States to work at the University of Rochester, Wisconsin and the City College of New York.

In 1969, soon after Gabriele Veneziano and Mahiko Suzuki discovered what became known as the “dual resonance model” or Veneziano model, Kikkawa collaborated with Bunji Sakita and Miguel Virasoro in Wisconsin to solve a vexing problem. The Veneziano amplitude miraculously satisfied many properties of the S-matrix, except one: unitarity.

To correct this, they made a radical and controversial conjecture. While most other groups tried to tinker with the Veneziano amplitude itself, the KSV group realized that it was actually the first-order Born term to an infinite sequence of multi-loop diagrams. Unitarity was then satisfied by sewing together an infinite number of Born terms. This was the origin of string perturbation theory, which today is the dominant method of extracting higher order information from string/M theory.

KSV conjectured what the multi-loop amplitudes might look like, by generalizing the duality of the Veneziano model. (Later, when Michio Kaku and others actually calculated the multi-loop amplitudes by brute force, it was found that the KSV rules were on the right track, but an infinite series of corrections had to be inserted into the multi-loop amplitude).

Later, it became apparent through the work of Yoichiro Nambu, Holger Nielsen, and Leonard Susskind that what was behind the dual resonance model was a vibrating string, thereby ushering in the next stage in its evolution. But this raised a nagging question: why was string theory so different from field theory? It was widely believed that a field theory formulation of string theory was not possible, since the Veneziano amplitude simultaneously included s- and t-channel exchanges, while Feynman diagrams included them separately. This was the “double-counting problem.”

Another problem was that there was no unified description of string theory in the language of fields. Since the time of Michael Faraday, physics could be described in the language of fields, so why was string theory so different?

In 1974, Kikkawa and Michio Kaku finally created the field theory of strings. In the KK paper, it was shown that in the light cone gauge, a string field theory did indeed add s- and t-channel pole as in Feynman diagrams, but that the sum of these two terms yielded precisely the Veneziano model.

Remarkably, string field theory could summarize all of string theory, including the Neveu-Schwarz-Ramond model, in a simple Lagrangian. Later, Edward Witten presented a fully relativistic formulation of the open bosonic string field theory. The relativistic bosonic closed string field theory was worked out by Michio Kaku and the Kyoto and MIT groups. (However, the covariant string field theory of superstrings has turned out to be considerably more complicated than previously thought).

But string theory faced yet another problem in its evolution. John Schwarz and Michael Green showed that there were 5 different superstring theories. The previous work of Tamiaki Yoneya, John Schwarz, and Joel Scherk showed that the theory naturally included general relativity, suggesting that string theory, instead of being a theory of hadrons, could be a “theory of everything.” But this left the puzzle: why should there be 5 different theories of everything?

Working with his student Masami Yamazaki, Kikkawa realized that there was yet another hidden property in string theory. If one took the string amplitude, compactified one dimension around a circle of radius R, the resulting amplitude was invariant under the strange substitution R -> 1/R. This meant that two string theories, which were apparently quite different, were actually the same in perturbation theory. This began what is called T-duality.

Very rapidly, a number of authors began to flesh out this duality. They found that T-duality showed that IIA and IIB string theories (and E(8) x E(8) and SO(32) strings) were the same under T-duality. Even more remarkable, Edward Witten and Petr Horava showed that Type IIA and E(8) x E(8) could be non-perturbatively dual to a mysterious, yet-unknown theory in 11 dimensions, called M-theory.

Kikkawa therefore made significant contributions to every stage of the evolution of string/M theory. We expect that string/M theory will have other stages and more surprises in its evolution. We regret that Kikkawa will not be with us to find them.

Michio Kaku
City College of New York
Takahiro Kubota
Osaka University
Tamiaki Yonyea
Open University of Japan