Canonical quantization of the string with dynamical geometry and anomaly free nontrivial string in two dimensions

TL;DR

This paper develops a canonical quantization framework for a two-dimensional string with dynamical geometry and torsion, demonstrating it is anomaly-free and has a consistent Fock space representation.

Contribution

It introduces a new canonical quantization of a string with dynamical geometry, showing the theory is anomaly-free and constructing novel Fock representations.

Findings

Existence of an anomaly-free Fock space for 2D gravity with torsion

Construction of a new Fock representation of the bosonic string

The string with dynamical geometry has two physical degrees of freedom

Abstract

Hamiltonian formulation of the string with dynamical geometry and two-dimensional gravity with torsion is given. Canonical Hamiltonian equals to the linear combination of first class constraints satisfying closed algebra. It is the semidirect sum of the Virasoro algebra and the abelian subalgebra corresponding to the local Lorentz rotation. After making the canonical transformation the theory is quantized. It is proved that there exists Fock space representation of pure two-dimensional gravity with torsion containing no central charge in the Virasoro algebra. Also constructed is the new Fock representation of a standard bosonic string. It is shown that two-dimensional string with dynamical geometry is anomaly free and describes two physical degrees of freedom.