Zero-Norm States and Superstringy Symmetries

TL;DR

This paper links zero-norm states in superstring theory to spacetime symmetries, providing evidence through multiple calculations and revealing new high-energy scattering amplitudes related to fermionic states.

Contribution

It identifies superstring spacetime symmetry charges from zero-norm states and extends high-energy symmetry analysis to superstrings, supporting and generalizing previous bosonic string results.

Findings

Identification of spacetime symmetry charges from zero-norm states

Support from supersymmetric sigma-model and 2D super-Liouville calculations

Discovery of new high-energy scattering amplitudes related to fermionic states

Abstract

We identify spacetime symmetry charges of the bosonic sector of 10D superstring theory from an infinite number of zero-norm states (ZNS) in the old covariant first quantized string spectrum. We give evidences to support this identification. These include supersymmetric sigma-model calculation, 2D super-Liouville theory calculation and, most importantly, three methods of high-energy scattering amplitude calculations. These calculations generalize the previous bosonic string calculations, which explicitly prove Gross's conjectures in 1988 on high energy symmetry of string theory. Moreover, we discover new high energy scattering amplitudes which are, presumably, related to the high energy massive spacetime fermionic scattering amplitudes in the R-sector of the theory.