# String total cross sections at asymptotically high energy

I only have a vague understanding of string theory, but a solid understanding of particle physics. At asymptotically high energy (Regge limit), the string cross section is dominated by the exchange of the leading trajectory -- the graviton trajectory, corresponding to an intercept $\alpha(0)=2$.

Regge phenomenology dictates that the string-string total cross should rise linearly with energy:

$$\sigma_\text{tot} \sim s^{\alpha(0)-1} = s$$

which is startling to me. Given that gravitons are massless, they are not subject to the Froissart-Martin bound $\sigma_\text{tot}<\log(s)^2$. So, is it really true that string-string total cross sections exhibit this growth?

An interpretation that was given to me by a fellow grad. student is that the open strings are 'forming a black hole,' with an area growing like $M^2 \sim s$. Is this correct?