Light-Cone Gauge Quantization of 2D Sigma Models

TL;DR

This paper develops a ghost-free light-cone gauge formulation for 2D bosonic string sigma models with non-trivial background fields, deriving conditions for Weyl invariance and exploring exactly solvable models.

Contribution

It introduces a manifestly ghost-free light-cone gauge approach for bosonic strings with complex backgrounds, including novel calculations of beta functions and critical dimensions.

Findings

Derived conditions for Weyl invariance in light-cone gauge

Calculated dilaton beta function and critical dimension in this framework

Discussed exactly solvable light-cone theories

Abstract

This work describes the formulation of the manifestly ghost-free (spacetime) light-cone gauge for bosonic string theory with non-trivial spacetime metric, antisymmetric tensor, dilaton and tachyon fields. The action is a general two-dimensional sigma model, corresponding to a closed string theory with a second order action in the Polyakov picture. The spacetime fields must have a symmetry generated by a null, covariantly constant spacetime vector in order for the light-cone gauge to be accessible. Also, the theory must be Weyl invariant. The conditions for Weyl invariance are computed within the light-cone gauge, reproducing the usual beta functions. The calculation of the dilaton beta function and the critical dimension is somewhat novel in this ghost-free theory. Some exactly solvable light-cone theories are discussed.