Bosonic string theory in background fields by canonical methods

TL;DR

This paper analyzes the classical dynamics of bosonic strings in various background fields using canonical methods, revealing new gauge symmetries and the effects of background fields on space-time geometry.

Contribution

It introduces a canonical approach to bosonic string theory in background fields, uncovering nonlinear Virasoro generators and new gauge symmetries involving both world-sheet and space-time variables.

Findings

Virasoro generators exhibit nonlinear realization due to the dilaton field.

Opposite chirality currents do not commute in curved space-time.

Background antisymmetric and dilaton fields induce torsion and nonmetricity in space-time.

Abstract

We investigate classical dynamics of the bosonic string in the background metric, antisymmetric and dilaton fields. We use canonical methods to find Hamiltonian in terms of energy-momentum tensor components. The later are secondary constraints of the theory. Due to the presence of the dilaton field the Virasoro generators have nonlinear realization. We find that, in the curve space-time, opposite chirality currents do not commute. As a consequence of the two-dimensional general covariance, the energy-momentum tensor components satisfy two Virasoro algebras, even in the curve space-time. We obtain new gauge symmetry which acts on both world-sheet and space-time variables, and includes world-sheet Weyl transformation. We emphasize that background antisymmetric and dilaton fields are the origin of space-time torsion and space-time nonmetricity, respectively.