Connection of Dual Models to Electrodynamics and Gravidynamics

Abstract

It is shown that the Virasoro-Shapiro model contains Einstein's theory of gravity as a zero-slope limit. It is also shown that the conventional dual model contains the scalar electrodynamics as a zero-slope limit. The connection between the generating functionals for the scattering matrices of these dual models and the corresponding field theories is demonstrated. § I. Introduction and summary It is widely believed that the slope parameter a m dual models has a fundamental meaning as a universal constant characterizing the unit of length. It is then of great interest to see what happens if one takes the limit a-40. This limit was first investigated by Scherk 1 l who showed that the conventional model reduces to the ¢ 3 Lagrangian theory in the limit with the ground-state mass and the quantity g 1..; a being fixed, where g is a dimensionless coupling constant of the model. This connection clarified in particular the correspondence 2 l between the usual F eynman diagrams and the duality diagrams. We believe that Scherk's work is an important step in understanding field theoretical foundations of dual models. On the· other hand, an essential feature of dual models is that the ghost states which appeared in the manifestly covariant factorization do decouple 3 l because of the built-in gauge invariance 4 l provided the intercepts are taken appropriately. The intercepts are such that the physical spectra of the models contain a massless spin 1-or 2+ state ("photon" or "graviton "). The Virasoro conditions 4 l are the reminiscences of the usual subsidiary conditions in quantum el'ectrodynamics and quantum gravidynamics. In fact, in appropriate zero-slope limits fixing the "photon" or the "graviton" states, some matrix elements of the former conditions are equivalent to the latter conditions. It is also remarkable that the photon vertices which play a crucial role in generating the algebras 5 l of the spectra are derived through a generalized local-gauge principle. 6 l-For these reasons, it will be more interesting to investigate the zero-slope limit fixing the intercepts at appropriate values. In fact, Neveu and Scherk 7 l pointed out that in such a limit the conventional model with the Chan-Paton isospin factor yields a massless Yang-Mills field theory of tree approximation.