The birth of string theory or how to build a theory without a Lagrangian

Paolo Di Vecchia | The Nordic Institute for Theoretical Physics 

Abstract:

I will start describing how the Veneziano 4-point amplitude and its generalisation to N-point, called Dual Resonance Model (DRM), were constructed using the basic properties of S-matrix theory. This procedure is opposite to the usual one where one constructs the S-matrix starting from a Lagrangian. In this case the S-matrix was constructed without knowing the corresponding Lagrangian. Only later it was shown that the S-matrix followed from the string Lagrangian.
Then I will discuss how the scattering amplitude was rewritten in terms of an infi nite set of harmonic oscillators that allowed to determine the spectrum of physical states and their scattering amplitudes. Absence of negative norm states, required by unitarity, restrict the intercept of the Regge trajectory to be equal to 1.
Already in 1970 Nambu, Nielsen and Susskind proposed that the underlying theory was a string theory, but it took few more years, by quantising the Nambu-Goto action in the light-cone gauge, to show that the spectrum of physical states coincided with the spectrum extracted from the DRM with $\alpha_0=1$.
Later it was shown that also the scattering amplitudes at tree and multiloop level were the same.
I will conclude discussing the attempt of writing the scattering amplitude for pions that brought instead to superstring. A string theory for pions is still absent. In modern language this will require to construct a string extension of the non-linear sigma-model that is the low-energy effective Lagrangian of QCD, but all attempts in this direction generated scattering amplitudes with negative norm states violating unitarity.
The only theories that allow for a string extension are the gauge theories and gravity and no string theory exists with one of the two without the other.

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