SPONTANEOUSLY BROKEN SYMMETRY IN STRING THEORY

Abstract

By using zero-norm states in the spectrum, we explicitly demonstrate the existence of an infinite number of high energy symmetry structures of the closed bosonic string theory. Each symmetry transformation (except those generated by massless zero-norm states) relates infinite particles with different masses, thus they are broken spontaneously at the Planck scale as previously conjectured by Gross and Evans and Ovrut. As an application, the results of Das and Sathiapalan which claim the sigma-model is nonperturbatively nonrenormalizable were reproduced from a stringy symmetry argument point of view.