The talk will provide a personal view of the emergence of string theory, its first two decades of development, and the research environment in which it occurred. The physical states of the Dual Resonance Model (DRM) of strong interactions, initiated by Veneziano in 1968, were quickly found to resemble those of a rubber band, though the dynamics differed. Nambu and Goto identified the correct string theory, whose quantization provided a precise physical picture for the DRM. As the building blocks of a complete theory—though not one describing the real world—were being assembled in the mid-1970s, attention was diverted by the successes of gauge theories. However, string theory continued to develop, becoming intertwined with conformal field theory and Kac-Moody algebras, leading to an explosion of interest in the mid-1980s.

I will talk about the puzzle that led to the suggestion of what is now called Peccei-Quinn symmetry, the path by which we came to our answer (still a viable one, best available but not necessarily right). The story includes a wrong conclusion we reached early in the work, how a conversation with Steve Weinberg showed us what was wrong and pointed to a better formulation of the problem, and what we still missed as we rushed to publish our idea. Key concepts include non-Abelian gauge theories of strong and weak interactions, the Higgs sector of the theory, CP symmetry and its breaking, the instanton-induced theta parameter, and axions.

Topological integrals of motion, magnetic monopoles in grand unification theories. Alice strings and Cheshire charge. Instantons. Atiyah-Singer index theorem, dimension of the space of instantons and Adler-Bell-Jackiw anomaly. Topological quantum field theories, Ray-Singer invariants, Chern-Simons theory, invariants of knots.

The first part of my talk will be on the work that I did during the transition period from the dual resonance model to string theory, while in the second part I will be presenting the 𝐶𝑃^(𝑁−1) model that was very important to finalize the low energy effective Lagrangian for the mesons in QCD. Then I will discuss how this Lagrangian solves the 𝑈(1) problem giving the spectrum of the pseudo-scalar mesons that we observe in the experiments. Finally, I will discuss the dependence of hadronic observables on the angle 𝜃 and extend this Lagrangian to also include the axion. In the final part of my talk I will remind my collaboration with Vadim Knizhnik who unfortunately died very young.

An account of some of the developments in conformal field theory as applied to condensed matter and statistical physics in the period from 1980 to 2010.

This will be a personal account of how the desire to construct some special models of string compactification led to the general idea of Rational Conformal Field Theory (RCFT). Then, how the desire to classify RCFTs led to the invention/discovery of the notion of a Modular Tensor Category (MTC), in work of G. Moore and N. Seiberg. Finally, it will address how MTCs were first applied to the idea that in 2+1 dimensions there can be particles that obey nonabelian statistics, in work of G. Moore and  N. Read. It must be stressed that this is not meant to be a definitive history, but rather is meant to provide primary material for a hypothetical future historian of science interested in the above topics.

Abstract: In the span of less than a year in 1984—1985, string theory blossomed into a unified theory of the fundamental forces, including gravity. We will review the development of theoretical physics up to this point, and how string theory organically grew from those developments yet radically transformed our understanding.