String tension ($T=(2\pi {\alpha }^{\prime }{)}^{-1}$)

String tension is energy per unit length. The Regge-slope parameter ${\alpha }^{\prime }$ is conventionally defined by $T=(2\pi {\alpha }^{\prime }{)}^{-1}$.

The characteristic string length is ${\ell }_s=\sqrt{{\alpha }^{\prime }}$, with $T=1/(2\pi {\alpha }^{\prime })$. Excited string states have masses of order $1/{\ell }_s$ and higher-derivative corrections become important at that scale.

A Regge trajectory is an approximately linear relation between angular momentum and squared mass. A classical rotating open string obeys $J={\alpha }^{\prime }{M}^2$, with quantum effects adding an intercept.

The Regge limit of a scattering amplitude takes the center-of-mass energy invariant $s$ large at fixed momentum-transfer invariant $t$. A leading trajectory produces a power $s^{\alpha (t)}$, with signature and residue factors. For the bosonic Virasoro–Shapiro amplitude in dimensionless string variables, $\alpha (t)=2+2t$. This differs from fixed-angle high-energy scattering.