String approaches to hadron structure

The two principal string approaches to a more realistic dual resonance model are discussed. Firstly, Nambu's proposal of 1974, identifying the Dirac magnetic-monopole string with the dual string, after spontaneous breakdown and the Higgs mechanism in a strong-coupling limit, is investigated. The mathematics underlying Nambu's rather intuitive derivation has been further investigated by Balachandran, Rupertsberger, and Schechter (who put in the vector mass by hand) and independently by Jevicki and Senjanovi$\stackrel{\mathrm{`}}{\mathrm{c}}$ (who fully exploit spontaneous breaking and the Higgs mechanism). Here we show that in a leading approximation to the Nambu monopole action the phenomenologically desirable linearity of the leading Regge trajectory seems to be badly violated. Secondly, alternative quantization procedures for the original 1970 Nambu relativistic string action (area of the world sheet) are treated; in particular, a timelike identification of the string time $\tau$ which has recently been advocated by Patrascioiu, by Rohrlich, and by Goddard, Hanson, and Ponzano. The most novel of these discussions seems to be that of Rohrlich, who uses a quite different representation for the canonical algebra and the Poincaré group. Here we demonstrate, however, that the usual unphysical level spectrum with a massless first excited state emerges as a fully consistent solution even in this approach, and that probably no other solution exists. Finally, the various Nambu string approaches are compared to other attempts to discover the "right" model of strong interactions.