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I have been study about Veneziano amplitude and Virasoro Shapiro amplitude. I want to summarize this two amplitude in the following way, please check that i am understand them properly.

Veneziano amplitude : they are open string amplitude for disk. Usually we called four-open string tachyon on disk as Veneziano amplitude

Virasoro-Shapiro amplitude : they are closed string amplitude for sphere. Usually we called four-closed string tachyons on shpere as Virasoro-Shapiro amplitude.

The similarity between Veneziano and Viraosoro-Shaprio amplitude are they both have Regge and hard scattering limit.


Is there are more difference and similarity for Veneziano and Virasoro-Shaprio amplitude?

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Well, there is the Kawai-Lewellen-Tye (KLT) relations, which says that a closed string amplitude is roughly speaking a product of two open string amplitudes. See e.g. Ref. 1.

References:

  1. Z. Bern, Perturbative Quantum Gravity and its Relation to Gauge Theory, Living Rev. Relativity 5 (2002) 5; Section 3.1.
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