2004 celebration of what the photographer Savdeep Sethi called the 20th anniversary of “the birth of string theory: namely the discovery of anomaly cancellation by Michael B. Green and John Schwarz.” Green is blowing out the candles while Schwarz looks on at an ACP picnic.

The Early Years of String Theory
at the Aspen Center for Physics

Michael B. Green, Cambridge University
John H. Schwarz, California Institute of Technology

We reminisce about some of the highlights in the development of string theory at the Aspen Center for Physics during the period 1969–1984, especially the authors’ collaboration in the period 1980–1984.

String theory emerged in the late 1960s as a candidate for understanding the strong interactions. For about five years it enlisted the efforts of several hundred young and enthusiastic theorists. The original “dual resonance model” is unrealistic in a number of respects: it describes bosons only and it requires 26 spacetime dimensions for its mathematical consistency. In 1971 a second string theory, this time containing fermions, arose from the work of Ramond [1] and Neveu and Schwarz [2]. This is sometimes referred to as the RNS string theory. As described below, the understanding of the structure of the RNS theory (especially its supersymmetry) increased over the years, and it evolved into a set of ten-dimensional “superstring” theories.

In the summer of 1974 JHS organized a string theory workshop at the ACP. It attracted many of the leading practitioners of that era. As it happened, this was shortly after the development of QCD and the Standard Model. Since QCD was recognized to be the correct theory of hadrons, and the known string theories had several features that were unrealistic for a theory of hadrons, interest in string theory was rapidly declining. Thus, this workshop turned out to mark the end of the first period of intense interest in string theory. It took a decade for string theory to reemerge, in a new guise, as an important area of research for the theoretical physics community.

In work carried out at Caltech in the Spring of 1974 Joël Scherk and JHS [3] proposed that the massless spin-two particle, which occurs as an excitation in the closed-string sector of consistent string theories, should be identified as the quantum of gravity, i.e., the graviton. Thus, the goal of string theory should be changed to constructing a unified quantum theory of all forces, including gravity, rather than just a theory of the hadrons. This was discussed at the 1974 workshop, but even in this select group only a few of the other participants (Lars Brink and David Olive, for instance) were motivated to pursue this idea at that time.

In 1976 Gliozzi, Scherk, and Olive discovered that, after a suitable projection, the RNS theory has an equal number of bosons and fermions at each mass level [4, 5]. This was strong evidence that the GSO-projected theory has ten-dimensional spacetime supersymmetry. Prior to this, it was only known that the two-dimensional string world sheet theory is supersymmetric — a fact that was influential in the origin of interest in supersymmetry.

In 1979 we began our collaboration, which had the initial goal of understanding the spacetime supersymmetry of the GSO-projected version of the RNS theory. During the subsequent five years, in addition to the time we spent at Caltech and Queen Mary College (University of London), we worked together most summers at the ACP. The highlights of our work included the following: the development of a new formalism in which the spacetimesupersymmetry of the GSO-projected RNS string is manifest [6, 14]; the classification of consistent ten-dimensional superstring theories, which we called type I, Type IIA, and Type IIB, and the finiteness of closed string one-loop graviton scattering amplitudes [9]; explicit calculation of various tree and loop amplitudes that illustrated various features of the theories [7, 8, 10]; development of light-cone gauge superstring field theory [11, 12, 13]. Each of these developments persuaded us that string theory had a compelling consistency that spurred us to investigate it further, but they did not seem to arouse much interest in the theory community. That changed following our next discovery.

It was understood in 1982 that Type I superstring theory is a well-defined ten-dimensional theory at tree level for any SO(n) or Sp(n) gauge group [15, 16]. However, in every case it is chiral (i.e., parity violating) and the open-string (gauge theory) sector is anomalous. Evaluation of a one-loop hexagon diagram exhibits explicit nonconservation of gauge currents, which is a fatal inconsistency. The only hope for consistency was that inclusion of the closed-string (gravitational) sector would cancel this anomaly without introducing new ones. An explicit computation was required to decide for sure.

In 1983 Luis Alvarez-Gaumé and Edward Witten derived general formulas for gauge, gravitational, and mixed anomalies in an arbitrary spacetime dimension [17], and they discovered that the gravitational anomalies (which would imply nonconservation of the stress tensor) cancel in type IIB supergravity and hence in type IIB superstring theory, which is therefore a consistent chiral superstring theory. If one hopes to make contact with the standard model, parity violation is an essential ingredient. However, the Type IIB theory did not look promising, since it does not seem to have any Yang–Mills gauge symmetry. (Many years later, it was understood that certain nonperturbative type IIB solutions do have Yang-Mills gauge symmetry.) Therefore the last hope seemed to reside with Type I superstring theories, which are chiral and do have Yang–Mills gauge symmetry.

The two of us explored the anomaly problem for type I superstring theory off and on for almost two years until the crucial breakthroughs were made in August 1984 at the Aspen Center for Physics. That summer JHS was the organizer of an ACP workshop entitled “Physics in Higher Dimensions.” This workshop attracted many participants, even though string theory was not yet fashionable, because by that time there was considerable interest in supergravity theories in higher dimensions and Kaluza–Klein compactification. Our research benefitted from the presence of many leading experts including Bruno Zumino, Bill Bardeen, Dan Friedan, and Steve Shenker.

We had tried previously to compute the one-loop hexagon diagram in type I superstring theory using our supersymmetric light-cone gauge formalism, but this led to an impenetrable morass, and the results were inconclusive. In discussions with Friedan and Shenker the idea arose to carry out the computation using the covariant RNS formalism instead. It soon became clear to us that both the cylinder and Möbius-strip world-sheet diagrams contributed to the anomaly. While walking to one of the workshop seminars, JHS remarked to MBG that there might be a gauge group for which the two contributions cancel. At the end of the seminar MBG said to JHS “SO(32),” which was the correct result. Since this computation only showed the cancellation of the pure gauge part of the anomaly, we decided to explore the low-energy effective field theory to see whether the gravitational and mixed anomalies could also cancel. Before long, using the results of Alvarez-Gaumé and Witten and helpful discussions with Bardeen and others, we were able to verify that all gauge, gravitational, and mixed anomalies cancel for the gauge group SO(32).

Shortly after these results were obtained, MBG left Aspen, while JHS remained for a few more weeks. One evening during that period the ACP organized a “Physics Cabaret” at the Hotel Jerome. This was the second (and last) such cabaret, the first having been held a decade earlier. On this occasion, JHS was asked to play the role that Murray Gell-Mann had played at the previous cabaret. In this role, JHS rushes unannounced onto the stage and announces that he has just discovered a theory of everything. Getting louder and louder, he continues that the Universe must have ten dimensions and supersymmetry, and that all matter is made up of little strings which have an SO(32) symmetry. At some point a man dressed in a white coat (Syd Meshkov) goes on stage and carries him off, even as he continues his ravings. Curiously, this was the first public announcement of our results.

In September, after we had arrived back at Caltech, we wrote up the effective field theory analysis of the anomaly cancellation [18]. (The string loop analysis of the anomaly, which we had actually done first, was written up a few months later [19].) This paper had a remarkable effect on a large segment of the theoretical particle physics community. Almost overnight, the subject became very hot. In fact, we felt that many of the new converts made a phase transition from being too pessimistic about this subject to being too optimistic about its near-term prospects for giving a complete realistic theory.

The effective field theory analysis showed that E8E8 is a second (and the only other) gauge group for which the anomalies could cancel for a theory with N = 1 supersymmetry in ten dimensions. In both cases, it is crucial for the result that the coupling to supergravity is included. The SO(32) case could be accommodated by type I superstring theory, but we didn’t know a superstring theory with gauge group E8E8: We were aware of the article by Goddard and Olive that pointed out (among other things) that there are exactly two even self-dual Euclidean lattices in 16 dimensions, and these are associated with precisely these two gauge groups [20]. However, we did not figure out how to exploit this fact before the problem was solved by others [21].

We end our narrative here by noting that there have been string theory workshops at the ACP almost every summer since 1984. We also wish to emphasize that we are extremely grateful for the stimulating and supportive environment that it provided for us.

[1] P. Ramond, “Dual Theory for Free Fermions,” Phys. Rev., D3, 2415 (1971).

[2] A. Neveu and J. H. Schwarz, “Factorizable Dual Model of Pions,” Nucl. Phys., B31, 86 (1971).

[3] J. Scherk and J. H. Schwarz, “Dual Models for Non-Hadrons,” Nucl. Phys., B81, 118 (1974).

[4] F. Gliozzi, J. Scherk, and D. Olive, "Supergravity and the Spinor Dual Model,” Phys. Lett., 65B, 282 (1976).

[5] F. Gliozzi, J. Scherk, and D. Olive, “Supersymmetry, Supergravity Theories and the Dual Spinor Model,” Nucl. Phys., B122, 253 (1977).

[6] M. B. Green and J. H. Schwarz, “Supersymmetrical Dual String Theory,” Nucl. Phys., B181, 502 (1981).

[7] M. B. Green and J. H. Schwarz, “Supersymmetrical Dual String Theory. 2. Vertices And Trees,” Nucl. Phys., B198, 252 (1982).

[8] M. B. Green and J. H. Schwarz, “Supersymmetrical Dual String Theory. 3. Loops and Renormalization,” Nucl. Phys., B198, 441 (1982).

[9] M. B. Green and J. H. Schwarz, “Supersymmetrical String Theories,” Phys. Lett., B109, 444 (1982).

[10] M. B. Green, J. H. Schwarz and L. Brink, “N = 4 Yang–Mills and N = 8 Supergravity as Limits of String Theories,” Nucl. Phys., B198, 474 (1982).

[11] M. B. Green and J. H. Schwarz, “Superstring Interactions,” Nucl. Phys., B218, 43 (1983).

[12] M. B. Green, J. H. Schwarz and L. Brink, “Superfield Theory of Type II Superstrings,” Nucl. Phys., B219, 437 (1983).

[13] M. B. Green and J. H. Schwarz, “Superstring Field Theory,” Nucl. Phys., B243, 475 (1984).

[14] M. B. Green and J. H. Schwarz, “Covariant Description of Superstrings,” Phys. Lett., B136, 367 (1984).

[15] J. H. Schwarz, “Gauge Groups for Type I Superstrings,” p. 233 in Proc. Johns Hopkins Workshop (1982).

[16] N. Marcus and A. Sagnotti, “Tree Level Constraints on Gauge Groups for Type I Superstrings,” Phys. Lett., B119, 97 (1982).

[17] L. Alvarez-Gaume and E. Witten, “Gravitational Anomalies,” Nucl. Phys., B234, 269 (1984).

[18] M. B. Green and J. H. Schwarz, “Anomaly Cancellation in Supersymmetric D = 10 Gauge Theory and Superstring Theory,” Phys. Lett., B149, 117 (1984).

[19] M. B. Green and J. H. Schwarz, “The Hexagon Gauge Anomaly in Type I Superstring Theory,” Nucl. Phys., B255, 93 (1985).

[20] P. Goddard and D. I. Olive, “Algebras, Lattices and Strings,” DAMTP-83/22.

[21] D. J. Gross, J. A. Harvey, E. J. Martinec and R. Rohm, “The Heterotic String,” Phys. Rev. Lett., 54, 502 (1985).