Spontaneously broken symmetry in string theory

TL;DR

This paper demonstrates the existence of an infinite set of high-energy symmetries in closed bosonic string theory using zero-norm states, revealing spontaneous symmetry breaking at the Planck scale and providing a stringy perspective on nonrenormalizability.

Contribution

It explicitly shows high-energy symmetries in string theory and explains their spontaneous breaking at the Planck scale using zero-norm states.

Findings

Infinite high-energy symmetry structures identified

Symmetries relate particles of different masses and are spontaneously broken

Stringy symmetry argument supports nonperturbative nonrenormalizability

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 that sigma-midel is nonperturbatively nonrenormalizable are reproduced from a stringy symmetry argument point of view.