The high energy behavior of open string scattering

Stringy symmetries and their high-energy limits

“…As a result, the high-energy scattering amplitudes of all string states can be expressed in terms of, say, the dilaton scattering amplitudes. A similar result was obtained for the open string by Gross and Manes [6]. However, the physical origin of these symmetries and thus the meaning of proportionality constants between the high-energy scattering amplitudes of different string states were unknown to those authors, and their values were not calculated.…”

“…(16) is gauge invariant as it should be since we derive it from Ward identities (5)- (8). On the other hand, the result obtained in [6] with T T T T ∝ T [LT ] , and T LLT = T (LT ) = 0 in the leading order energy at this mass level is, on the contrary, not gauge invariant. In fact, with only two non-zerΣo amplitudes of T T T T and T [LT ] , an inconsistency arises between eqs.…”

“…We will justify this point later in our sample calculation. Our calculation here is, similar to the toy 2D string case, purely algebraic without any integration and is independent of saddle point calculation in [3,5,6]. It is important to note that our result in eq.…”

“…To produce Gross's high-energy result and fix the proportionality constants, which were not dwelt on in Ref [3,6] due to lack of the physical origin of the proposed highenergy symmetries, one needs to calculate high-energy limit of eqs. (5)- (8).…”

“…(5)- (8) without referring to the saddle point calculation in [3,5,6]. Let's define the normalized polarization vectors,e P = 1…”