Physical States and String Symmetries

TL;DR

The paper demonstrates that string theory states with lattice momenta induce symmetries in scattering amplitudes, revealing the Fake Monster Lie algebra as a symmetry in certain compactifications.

Contribution

It shows that physical string states with lattice momenta generate symmetries in scattering amplitudes, linking string compactification to the Fake Monster Lie algebra.

Findings

States with lattice momenta induce amplitude symmetries

Fake Monster Lie algebra appears as a symmetry in specific compactifications

Symmetries relate to the D.D.F construction and self-dual lattices

Abstract

It is shown that if the momenta belong to an integral lattice, then every physical state of string theory leads to a symmetry of the scattering amplitudes. We discuss the role of this symmetry when the momenta are those provided by the usual D.D.F construction and show that the string compactified on the torus associated with the self-dual Lorentzian lattice, $\Pi^{25,1}$ possess the Fake Monster Lie algebra as a symmetry.