Veneziano amplitude

In theoretical physics, the Veneziano amplitude refers to the discovery made in 1968 by Italian theoretical physicist Gabriele Veneziano that the Euler beta function, when interpreted as a scattering amplitude, has many of the features needed to explain the physical properties of strongly interacting mesons, such as symmetry and duality.^[1] Conformal symmetry was soon discovered. This discovery can be considered the birth of string theory,^[2] as the invention of string theory came about as a search for a physical model which would give rise to such a scattering amplitude. In particular, the amplitude appears as the four tachyon scattering amplitude in oriented open bosonic string theory. Using Mandelstam variables and the beta function ${\displaystyle B(x,y)}$, the amplitude is given by^[3]

${\displaystyle S(k_{1},k_{2},k_{3},k_{4})={\frac {2ig_{o}^{2}}{\alpha '}}(2\pi )^{26}\delta ^{26}(\Sigma _{i}k_{i}){\big [}B(\alpha (s),\alpha (t))+B(\alpha (s),\alpha (u))+B(\alpha (t),\alpha (u)){\big ]}}$

where ${\displaystyle \alpha '}$ is the string constant, ${\displaystyle k_{i}}$ are the tachyon four-vectors, ${\displaystyle g_{o}}$ is the open string theory coupling constant, and ${\displaystyle \alpha (x)=-1-\alpha 'x}$.

See also

• Beta function
• Crossing (physics)
• Dual resonance model
• History of string theory
• Regge theory

References

1. Veneziano, G. (1968). "Construction of a crossing-symmetric, Regge-behaved amplitude for linearly rising trajectories". Nuovo Cimento A. 57 (1): 190–7. Bibcode:1968NCimA..57..190V. doi:10.1007/BF02824451.
2. Di Vecchia, P. (2008). "The Birth of String Theory". In Gasperini, Maurizio; Maharana, Jnan (eds.). String Theory and Fundamental Interactions – Gabriele Veneziano and Theoretical Physics: Historical and Contemporary Perspectives. Lecture Notes in Physics. Vol. 737. Springer. pp. 59–118. doi:10.1007/978-3-540-74233-3_4. ISBN 978-3-540-74232-6. arXiv preprint
3. Polchinski, J. (1998). "6". String Theory Volume I: An Introduction to the Bosonic String. Cambridge University Press. p. 183. ISBN 978-0143113799.

External links

• String Theory and M-Theory, Lecture 6, Video lecture by Leonard Susskind on Veneziano amplitude. (Stanford University)