Vertex operator expressions for Lie algebras of physical states (2408.07597v1)

Abstract: We study the Lie algebra of physical states associated with certain vertex operator algebras of central charge 24. By applying the no-ghost theorem from string theory we express the corresponding Lie brackets in terms of vertex algebra operations. In the special case of the Moonshine module this result answers a question of Borcherds, posed in his paper on the Monstrous moonshine conjecture.