Speaker
Description
I will start by describing how the Veneziano four-point amplitude and its generalization to N-point amplitudes, known as the Dual Resonance Model (DRM), were constructed using the basic principles of S-matrix theory. This approach is the opposite of the usual procedure, in which one derives the S-matrix from a Lagrangian. In this case, the S-matrix was constructed without knowledge of the corresponding Lagrangian, which was identified only later as the string Lagrangian.
I will then discuss how the scattering amplitudes were reformulated in terms of an infinite set of harmonic oscillators, making it possible to determine the spectrum of physical states and their scattering amplitudes. The requirement of unitarity, namely the absence of negative-norm states, restricts the intercept of the Regge trajectory to be equal to one.
As early as 1970, Nambu, Nielsen, and Susskind proposed that the underlying theory was a string theory. However, it took several more years—and the quantization of the Nambu–Goto action in the light-cone gauge—to demonstrate that the spectrum of physical states coincided with that extracted from the DRM with α₀ = 1. It was subsequently shown that the tree-level and multiloop scattering amplitudes also agreed.
I will conclude by discussing attempts to construct scattering amplitudes for pions, which instead led to the development of superstring theory. A string theory for pions is still lacking. In modern terms, this would require a string extension of the nonlinear sigma model, the low-energy effective theory of QCD. However, all attempts in this direction have produced scattering amplitudes containing negative-norm states, thereby violating unitarity.
The only theories known to admit a consistent string extension are gauge theories and gravity, and no string theory exists that contains one without the other. In conclusion, what began as an attempt to construct an S-matrix for mesons ultimately led instead to a theory unifying gauge interactions and gravity.