Dual resonance models and their currents

It is shown how dual resonance models were rederived from the concept of a string tracing out a surface in space-time. Thus, interacting strings reproduce the dual amplitudes. A scheme for tackling the unitarity problem began to develop. As a consistent theory of hadronic processes began to be built, workers at the same time were naturally led to expect that leptons could be included with hadrons in a unified dual theory. Thus, there is a search for dual amplitudes which would describe interactions between hadrons and currents (for example, electrons), as well as interactions involving only hadrons. Such amplitudes, it is believed, will be the correct ones, describing the real world. Such amplitudes will provide valuable information concerning such things as hadronic form factors. The great difficulties in building current-amplitudes with the required properties of proper factorization on a good spectrum, duality, current algebra, and proper asymptotic behavior are described. Dual models at the present time require for consistency, an intercept value of α0 = 1 and a dimension value of d = 26 (or d = 10). There have been speculations that the unphysical dimension may be made physical by associating the ''extra dimensions'' with certain internal degrees of freedom. However, it is desired that the theory itself, force the dimension d = 4. It is quite possible that the dimension problem and the intercept problem are tied together and that resolving either problem will resolve the other. Order by order, a new dual current is constructed that is manifestly factorizable and which appears to be valid for arbitrary space-time dimension. The fact that this current is not bound at d = 26, leads to interesting speculations on the nature of dual currents