Comments on the global constraints in light-cone string and membrane theories

TL;DR

This paper examines the global constraints in light-cone string and membrane theories, revealing their gauge symmetry roles, implications for physical states, and behavior of ghosts, with insights into membrane reduction.

Contribution

It clarifies the nature of global constraints as gauge symmetries and analyzes their effects on physical states and ghost fields in light-cone string and membrane theories.

Findings

Physical states satisfy level-matching condition.

Ghosts are free regardless of gauge fixing.

Discusses quantum reduction of supermembrane.

Abstract

In the light-cone closed string and toroidal membrane theories, we associate the global constraints with gauge symmetries. In the closed string case, we show that the physical states defined by the BRS charge satisfy the level-matching condition. In the toroidal membrane case, we show that the Faddeev-Popov ghost and anti-ghost corresponding to the global constraints are essentially free even if we adopt any gauge fixing condition for the local constraint. We discuss the quantum double-dimensional reduction of the wrapped supermembrane with the global constraints.