Discrete States of 2D String Theory in Polyakov's Light-Cone Gauge

TL;DR

This paper identifies the discrete physical states of the c=1 string in Polyakov's light-cone gauge, revealing differences from the conformal gauge and emphasizing the physical nature of these states.

Contribution

It demonstrates the equivalence of light-cone and conformal gauges using Wakimoto free-field representation, clarifying the physicality of discrete states in the theory.

Findings

States with ghost numbers up to 4 appear in the cohomology.

The light-cone and conformal gauges are equivalent in the Wakimoto representation.

Natural states do not satisfy KPZ constraints.

Abstract

We find the discrete states of the c=1 string in the light-cone gauge of Polyakov. When the state space of the gravitational sector of the theory is taken to be the irreducible representations of the SL(2,R) current algebra, the cohomology of the theory is NOT the same as that in the conformal gauge. In particular, states with ghost numbers up to 4 appear. However, after taking the space of the theory to be the Fock space of the Wakimoto free-field representation of the SL(2,R), the light-cone and conformal gauges are equivalent. This supports the contention that the discrete states of the theory are physical. We point out that the natural states in the theory do not satisfy the KPZ constraints.