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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 emphasize that background antisymmetric and dilaton fields are the origin of space–time torsion and space–time nonmetricity, respectively. [ABSTRACT FROM AUTHOR]

Using canonical method the Liouville theory has been obtained as a gravitational Wess-Zumino action of the Polyakov string. From this approach it is clear that the form of the Liouville action is the consequence of the bosonic representation of the Virasoro algebra, and that the coefficient in front of the action is proportional to the central charge and measures the quantum braking of the classical symmetry. [ABSTRACT FROM AUTHOR]