nLab Veneziano amplitude

Idea

The Veneziano amplitude is the tree-level string scattering amplitude for the scattering of four open bosonic strings in their tachyon states. Hence equivalently it is a certain 4-point function in a certain boundary 2d CFT.

Historically, this amplitude first arose in dual resonanace models? and the realization that it has a natural interpretation as the scattering of strings was one of the main original motivations for the development of string theory.

Related concepts

• Virasoro amplitude

• In p-adic string theory (see there) one considers adelic integral-variants of the Veneziano amplitude.

• vacuum amplitude

References

• Michael Green, John Schwarz, Edward Witten, section 1.1 of Superstring theory Volume 1, Cambridge Monographs on Mathematical Physics, 1987

• Gerard 't Hooft, section 1.2 and section 6 of Introduction to string theory 2004 (pdf)

• The Veneziano amplitude pdf

Discussion in the context of Riemann hypothesis and physics is in

• Yang-Hui He, Vishnu Jejjala, Djordje Minic, From Veneziano to Riemann: A String Theory Statement of the Riemann Hypothesis (arXiv:1501.01975)

Textbook review includes (16.49) in

• Ralph Blumenhagen, Dieter Lüst, Stefan Theisen, String Scattering Amplitudes and Low Energy Effective Field Theory, chapter 16 in Basic Concepts of String Theory Part of the series Theoretical and Mathematical Physics pp 585-639 Springer 2013

See also:

• Clifford Cheung, Grant N. Remmen, Veneziano Variations: How Unique are String Amplitudes? [arXiv:2210.12163]

• Nicholas Geiser, Lukas W. Lindwasser, Generalized Veneziano and Virasoro amplitudes [arXiv:2210.14920]