Light-Cone Gauge for 1+1 Strings

TL;DR

This paper constructs a light-cone gauge quantum theory for 1+1 dimensional bosonic strings, revealing unexpected algebraic structures, residual symmetries, and conditions for BRST charge nilpotency, while discussing challenges in maintaining Lorentz invariance.

Contribution

It introduces a novel gauge choice that yields a free action with ghosts and residual symmetries, and demonstrates BRST charge nilpotency in a linear dilaton background.

Findings

Existence of a gauge with free action and residual U(1) symmetry.

BRST charge is nilpotent with a linear dilaton background.

Spacetime Lorentz invariance remains unresolved.

Abstract

Explicit construction of the light-cone gauge quantum theory of bosonic strings in 1+1 spacetime dimensions reveals unexpected structures. One is the existence of a gauge choice that gives a free action at the price of propagating ghosts and a nontrivial BRST charge. Fixing this gauge leaves a U(1) Kac-Moody algebra of residual symmetry, generated by a conformal tensor of rank two and a conformal scalar. Another is that the BRST charge made from these currents is nilpotent when the action includes a linear dilaton background, independent of the particular value of the dilaton gradient. Spacetime Lorentz invariance in this theory is still elusive, however, because of the linear dilaton background and the nature of the gauge symmetries.