Revival of the Old String Model

Abstract

In this talk I would like to review the recent developments in the theory of strings induced by a novel approach due to Polyakov.^1,2 The “old” string model³ of the early seventies had some severe problems that allowed a consistent treatment only when the space time dimensionality is 26. The important observation was that due to coordinate transformations invariance, also called “gauge” invariance, of the Nambu action, there are relations or constraints among the coordinates and momenta. In order to quantize the theory canonically, one can either eliminate redundant degrees of freedom and quantize noncovariantly or quantize covariantly and impose the constraints on the physical states. It turned out that in the first method, Lorentz covariance was recovered only in d=26, and in the second approach “ghost” states could be eliminated only at d = 26. In this space-time dimensionality both methods agree. But of course we are looking for a string theory which can be quantized in four dimensions.* Another problem of the “old” string model was the appearance of “tachyons” with imaginary mass.