Stringy scaling of multi-tensor hard string scattering amplitudes and the K-identities

A bstract We calculate n -point hard string scattering amplitudes ( HSSA ) with n − 2 tachyons and 2 tensor states at arbitrary mass levels. We discover the stringy scaling behavior of these HSSA . It is found that for HSSA with more than 2 transverse directions, the degree of stringy scaling dim $$\mathcal{M}$$ 2 decreases comparing to the degree of stringy scaling dim $$\mathcal{M}$$ 1 of the n − 1 tachyons and 1 tensor HSSA calculated previously. Moreover, we propose a set of K -identities which is the key to demonstrate the stringy scaling behavior of HSSA . We explicitly prove both the diagonal and off-diagonal K -identities for the 4-point HSSA and give numerical proofs of these K -identities for some higher point HSSA .