Zero-norm states and high-energy symmetries of string theory Original Research Article

We derive stringy Ward identities from the decoupling of two types of zero-norm states in the old covariant first quantized (OCFQ) spectrum of open bosonic string. These Ward identities are valid to all energy α′ and all loop orders χ in string perturbation theory. The high-energy limit α′→∞ of these stringy Ward identities can then be used to fix the proportionality constants between scattering amplitudes of different string states algebraically without referring to Gross and Mendeʹs saddle point calculation of high-energy string-loop amplitudes. As examples, all Ward identities for the mass level M2=4,6 are derived, their high-energy limits are calculated and the proportionality constants between scattering amplitudes of different string states are determined. In addition to those identified before, we discover some new nonzero components of high-energy amplitudes not found previously by Gross and Manes. These components are essential to preserve massive gauge invariances or decouple massive zero-norm states of string theory. A set of massive scattering amplitudes and their high-energy limits are calculated explicitly for each mass level M2=4,6 to justify our results.