Higher Order Action for the Interaction of the String with the Dilaton

TL;DR

This paper analyzes the interaction of a string with a dilaton background, developing a canonical formalism that reveals the constraints and physical degrees of freedom, and computes the physical Hamiltonian in the light cone gauge.

Contribution

It introduces a higher order action for string-dilaton interaction, develops the canonical formalism, and explicitly computes the physical Hamiltonian in the light cone gauge.

Findings

Identifies first and second class constraints in the theory.

Shows the degrees of freedom match those of the free bosonic string.

Derives the physical Hamiltonian in the light cone gauge.

Abstract

The theory of the string in interaction with a dilaton background field is analyzed. In the action considered, the metric in the world sheet of the string is the induced metric, and the theory presents second order time derivatives. The canonical formalism is developed and it is showed that first and second class constraints appear. The degrees of freedoom are the same than for the free bosonic string. The light cone gauge is used to reduce to the physical modes and to compute the physical hamiltonian.