One knows the formula for the open string $4$-tachyon amplitude for the disk topology in the bosonic string theory : it is proportortionnal to the $s \leftrightarrow t \leftrightarrow u$ symmetrisation of the Veneziano amplitude $B(- \alpha's-1, - \alpha't-1)$.

However, what is the explicit value of the open string $4$-tachyon (one-loop) amplitude for the cylinder/annulus topology in the bosonic string theory ?

If possible, what is the expression of this amplitude in a serie of poles of $s$ or $t$, analogeous to the known series for the Veneziano amplitude ?

This post imported from StackExchange Physics at 2014-10-02 12:02 (UTC), posted by SE-user Trimok