11 - From the S-matrix to string theory

Summary

Abstract

In this Chapter I describe the ideas and developments that led to the recognition that the structure underlying the N-point scattering amplitude of the Dual Resonance Model was that of a quantum-relativistic string.

Introduction

The history of the origin of string theory is very peculiar and difficult to understand if one looks at it with today's eyes. In particular, the fact that one could understand so many string properties without making reference to any Lagrangian, and without even knowing that one was studying a string, seems almost miraculous.

In fact, the starting point for describing the property of a relativistic string is today the string Lagrangian, which is invariant under reparameterizations of the world-sheet coordinates. From it, using techniques developed for quantizing theories with local gauge invariance, such as the Faddeev–Popov and the BRST quantization, one derives the spectrum of physical states and their scattering amplitudes. However, at the end of the Sixties and at the beginning of the Seventies, these techniques were not yet known and, even though the Nambu–Goto action had already been written, it was not clear how to use it to deduce its physical consequences. Therefore, the historical path that led us to understand the properties of a relativistic string was quite different from the path that one follows today, for instance, when teaching string theory in a university course. But at that time, where did string theory come from?