Reaction amplitude for n-mesons a generalization of the Veneziano-Bardakçi-Ruegg-Virasoro model

On modified tachyon DBI action

“…The number of independent kinematic factors in the scattering amplitude of n states is n 2 (n − 3) [26]. In the present case, there are 5 independent kinematic factors.…”

All-order collinear behavior in gauge theories

“…This form may be derived from either the Berends-Giele recurrence relations [17], or else [18] from the Koba-Nielsen open-string amplitude [19]. Either derivation shows that this factorization holds only for on-shell (that is, physically polarized) legs a, b, but in arbitrary dimension.…”

Erratum to “Open strings”

“…A possible solution of the R-R tadpole conditions is n = 13, m = 3, d = 4, that corresponds to a gauge group of rank 20, U(13) 9 × U(3) 9 × U(4) 5 , with charged hyper multiplets in the representations (78 + 78, 1, 1), in five copies of the (1, 3 + 3, 1), in one copy of the (1, 1, 6 + 6), in four copies of the (13,3,1), in one copy of the (13,1,4) and in one copy of the (1,3,4). Alternatively, one can take n = 14, m = 2, d = 8, obtaining a gauge group of rank 24, U(14) 9 × U(2) 9 × U(8) 5 .…”

“…The celebrated Veneziano formula [1] for open-string tachyons, that marked the birth of String Theory in the form of "dual models" for hadron resonances, was shortly followed by the Shapiro-Virasoro formula for closed-string tachyons [2] and by their multi-particle generalizations [3], as well as by the Neveu-Schwarz-Ramond fermionic string [4]. The early work of the following decade provided the foundations for the subject [5], whose very scope took a sharp turn toward its current interpretation as a theory of the fundamental interactions only at the end of the seventies, some time after Scherk and Schwarz and Yoneya [6] elucidated the close link between the lowenergy behaviour of string amplitudes on the one hand, and higher-dimensional gauge theories and gravity on the other.…”