Perturbative unitarity of dual loops

Two-loop chiral anomalies in open superstrings

“…In analogy with previous work in string theory, we assume all seven class (A) and the two class (B) diagrams must be added with equal weight to preserve unitarity. 8,9 It is gratifying that when this is done in D dimensions we get precisely the same (N -2 D/2 ) factor to cancel the leading gauge anomaly as was obtained at one loop.…”

“…A similar new term is likely to appear in the 0(32) heterotic string, presumably from a different part of the integration region for the double torus. For E($)®E (8),…”

From dual models to relativistic strings

“…I began my own efforts by trying to understand the details of how the Veneziano model, together with the higher loop amplitudes that were being constructed, would provide a formal perturbative solution to the unitarity equations [21]. There was, however, what looked like a fly in the ointment.…”

“…It was not that anyone in Cambridge, in those days before asymptotic freedom, thought that perturbative quantum field theory would be directly relevant to strong interaction physics (as far as I know), rather that it provided a formal solution to the unitarity conditions and, in a certain sense, exhibited Regge high energy behavior. I began my own efforts by trying to understand the details of how the Veneziano model, together with the higher loop amplitudes that were being constructed, would provide a formal perturbative solution to the unitarity equations [21]. There was, however, what looked like a fly in the ointment.…”