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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 , the amplitude is given by^{[3]}

where is the string constant, are the tachyon four-vectors, is the open string theory coupling constant, and .

**^**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.**^**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**^**Polchinski, J. (1998). "6".*String Theory Volume I: An Introduction to the Bosonic String*. Cambridge University Press. p. 183. ISBN 978-0143113799.

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