# Dual resonance model

In theoretical physics, a dual resonance model arose during the early investigation (1968–1973) of string theory as an S-matrix theory of the strong interaction.

## Overview

The dual resonance model was based upon the observation that the amplitudes for the s-channel scatterings matched exactly with the amplitudes for the t-channel scatterings among mesons and also the Regge trajectory. It began with the Euler beta function model of Gabriele Veneziano in 1968 for a 4-particle amplitude which has the property that it is explicitly s–t crossing symmetric, exhibits duality between the description in terms of Regge poles or of resonances, and provides a closed-form solution to non-linear finite-energy sum rules relating s- and t- channels.

The Veneziano formula was quickly generalized to an equally consistent N-particle amplitude[1] for which Yoichiro Nambu,[2] Holger Bech Nielsen,[3] and Leonard Susskind[4] provided a physical interpretation in terms of an infinite number of simple harmonic oscillators describing the motion of an extended one-dimensional string, hence came the name "string theory."

The study of dual resonance models was a relatively popular subject of study between 1968 and 1973.[5] It was even taught briefly as a graduate level course at MIT, by Sergio Fubini and Veneziano, who co-authored an early article.[6] It fell rapidly out of favor around 1973 when quantum chromodynamics became the main focus of theoretical research[7] (mainly due to the theoretical appeal of its asymptotic freedom).[8]

## Notes

1. ^ Koba, Z. and Nielsen, H. (1969). "Reaction amplitude for N-Mesons: A generalization of the Veneziano-Bardakçi-Ruegg-Virasoro model." Nuclear Physics, B10, 633–655.
2. ^ Nambu, Y. (1970). "Quark model and the factorization of the Veneziano amplitude." In R. Chand (ed.), Symmetries and quark models (pp. 269–277). Singapore: World Scientific.
3. ^ Nielsen, H. B. "An almost physical interpretation of the dual N point function." Nordita preprint (1969); unpublished.
4. ^ Susskind, L. (1969). "Structure of hadrons implied by duality." Physical Review D, 1(4), 1182–1186.
5. ^ Rickles 2014, pp. 5–6, 44.
6. ^ S. Fubini and G. Veneziano, "Level Structure of Dual Resonance Models", Il Nuovo Cimento 64A (1969) 811.
7. ^ Rickles 2014, p. 77.
8. ^ Rickles 2014, p. 11 n. 22.

## References

• Dean Rickles (2014). A Brief History of String Theory: From Dual Models to M-Theory. Springer. ISBN 978-3-642-45128-7.