Zero-norm states and stringy symmetries

Abstract

We identify spacetime symmetry charges of string theory from an infinite number of zero-norm states (ZNS) with arbitrary high spin in the old covariant first quantized string spectrum. We give various evidences to support this identification. These include massive sigma-model calculation, Witten string field theory calculation, 2D string theory calculation and, most importantly, three methods of high-energy stringy scattering amplitude calculation. The last calculations explicitly prove Gross\'s conjectures in 1988 on high energy symmetry of string theory.