We investigate the relation between the factorization schemes in previously proposed Feynman-like rules for the Veneziano model and the gauge freedom in the massless YangMills field. We consider the case of the unit intercept and introduce to our rules the ChanPaton U(2) factors. By taking a zero-slope limit of the Feynman-like rules in two different _factorization schemes, we derive two forms of the Feynman rules for the massless YangMills field. One of them is in the usual Feynman gauge and the other is in a special nonhermitian gauge which, has been proposed by Gervais and Neveu. It turns out that the zero-slope limit of the usual off-mass-shell n-Reggeon vertex has a peculiar feature which cannot be described by Lagrangians. Nevertheless, we show that the on-mass-shell physical amplitudes can be described by Lagrangians. The investigations are confined in the tree approximation. § l. Introduction It is known that there is a considerable degree of freedom in factorizing the dual resonance amplitudes. The existence of such freedom reminds us of the gauge freedom in gauge :field theories. A very general single-factorization scheme which has this freedom was proposed by Shapiro. 1 l This scheme was further extended to general n-ple factorization in an earlier paper 2 l of the present author,· which is hereafter referred to as I. On the other hand, interesting relationships between the dual models and the gauge :field theories have been established for some zero-slope limits 3 l~a) of the dual models. However, the connection between those two different theoretical programs is shown only for the S-matrix elements. It is of some interest to seek more structural correspondences between th~m. The purpose, of the present note is to investigate the zero-slope limit in detail and to establish the connection of the general factorization scheme developed in I with the gauge freedom of the massless Yang-Mills :field. In studying the zero-slope limits, it is very convenient to use the Feynman-like rules based on the Nakanishi decomposition 7 l of the dual amplitude, which was proposed in another paper 8 l referred to hereafter as II. According to these rules, the topological structure and the counting_ of graphs are identical with those of the ordinary ¢ 3 -F eynman graphs. In this note, we consider the zero-slope limit a' ~o of the Veneziano model with the Chan-Paton isospin factors, keeping the Regge intercept a (0) equal to one instead of setting -a (0) =a' m 2 • We then demonstrate how
First I went back to the connection of open strings to non-Abelian gauge theory, and decided to establish a detailed connection at the level of Feynman rules REF on the basis of my previous work on the general Reggeon vertex and the Nakanishi decomposition.
Gauge Freedom in Dual Feynman-Like Rules and Its Relation to the Massless Yang-Mills Field Theory
Progress of Theoretical Physics
Physics