In the talk that I gave in Chicago with David Gross in the chair, I mentioned both the Yang-Mills theory—essentially quantum chromodynamics—and the string version of it, a possible string version of it, we didn't know exactly what that would look like. But I didn't emphasize it very much and in the written version we just sort of glossed over it, because we were worried about these three points. But later on Fritzsch and Leutwyler and I took up this matter in a… a letter that we wrote in 1973, from Aspen. We were all in Aspen, Colorado together, and there we took up what I referred to out of… or… out of its proper place a moment ago, which was the problem of the ninth axial vector current and the corresponding pseudo-scalar boson. And this–since it's a bit complicated–let me read again from what I wrote in that paper:
We discussed in the limit of vanishing quark masses, conservation of the flavor singlet axial vector current which threatens to yield four light pseudo-scalar mesons instead of three in the case of SU(2) of flavor, and nine instead of eight for SU(3) of flavor, contrary to fact. That was an old preoccupation of mine. Does the divergence of the axial vector current, the ninth axial vector current or the fourth axial vector current, actually go to zero as the masses go to zero? Theory seemed to have that difficulty. But there's an anomaly in the theory proportional to a term bilinear in the gluon fields. But the anomaly term itself is the divergence of another current, so if we add that current to the axial vector current, we still have the divergence of a current going to zero as mass going to zero, which seems to give the difficulty back in another form. But there were two more ‘buts’, fortunately an even number that we didn't cover in our letter. The charge integral J naught five b cubed x does appear to be gauge invariant and the time derivative of the total charge seems to go to zero as the masses go to zero, and that's apparently gauge invariant. But, as was shown by Polyakov and company and by 't Hooft in connection with instantons, this charge is only locally but not globally gauge invariant. So in fact, there's no problem of a fourth or a ninth light pseudo-scalar boson.