Classical and quantum massive string

TL;DR

This paper explores a modified massive string model, analyzing its classical and quantum properties across various dimensions, and establishes its equivalence to known string theories under specific conditions.

Contribution

It introduces a modified BDHP action for massive strings, provides a detailed classical and quantum analysis, and demonstrates equivalence to other string models at critical parameter values.

Findings

Classical solutions analyzed in target space geometry.

Quantum theory constructed with DDF operators and no-ghost theorem proved.

At a critical parameter, the model is equivalent to the noncritical Polyakov string.

Abstract

The classical and the quantum massive string model based on a modified BDHP action is analyzed in the range of dimensions $1<d<25$. The discussion concerning classical theory includes a formulation of the geometrical variational principle, a phase-space description of the two-dimensional dynamics, and a detailed analysis of the target space geometry of classical solutions. The model is quantized using "old" covariant method. In particular an appropriate construction of DDF operators is given and the no-ghost theorem is proved. For a critical value of one of free parameters of the model the quantum theory acquires an extra symmetry not present on the classical level. In this case the quantum model is equivalent to the noncritical Polyakov string and to the old Fairlie-Chodos-Thorn massive string.