$D=2$ String Theory in Target Space/World-Sheet Light-Cone Gauge

TL;DR

This paper investigates a two-dimensional string theory in a specific gauge, revealing that its physical spectrum is trivial in the standard vacuum but becomes nontrivial when considering different representations of the conformal field theory algebra.

Contribution

It introduces a detailed analysis of the $D=2$ string in target space/world-sheet light-cone gauge, highlighting the role of different CFT representations in the physical spectrum.

Findings

Physical spectrum is trivial in $SL_2$ invariant vacuum.

Nontrivial spectrum emerges when considering different CFT representations.

Residual symmetries include Virasoro and $U(1)$ current.

Abstract

$D=2$ free string in linear dilaton background is considered in so called target space/world-sheet light cone gauge $ X^{+}=0,~g_{++}=0,~g_{+-}=1$. After gauge fixing the theory has the residual Virasoro and $U(1)$ current symmetries. The physical spectrum related to $SL_2$ invariant vacuum is found to be trivial. We find that the theory has a nontrivial spectrum if the states in different non-equivalent representations ("pictures") of CFT algebra of matter fields are considered.