Variational principle and a perturbative solution of non-linear string equations in curved space

TL;DR

This paper develops a perturbative approach to analyze string dynamics in curved spacetime, deriving covariant equations that reduce to geodesic equations at first order and solving them for specific cosmological backgrounds.

Contribution

It introduces a variational principle and a perturbative solution method for non-linear string equations in curved space, extending known geodesic equations with oscillatory terms.

Findings

Derived covariant non-linear string equations in curved spacetime

Solved equations for de Sitter and Friedmann-Robertson-Walker spaces

Established stability of string dynamics in de Sitter space for large Hubble constant

Abstract

String dynamics in a curved space-time is studied on the basis of an action functional including a small parameter of rescaled tension $\epsilon=\gamma/\alpha^{\prime}$, where $\gamma$ is a metric parametrizing constant. A rescaled slow worldsheet time $T=\epsilon\tau$ is introduced, and general covariant non-linear string equation are derived. It is shown that in the first order of an $\epsilon $-expansion these equations are reduced to the known equation for geodesic derivation but complemented by a string oscillatory term. These equations are solved for the de Sitter and Friedmann -Robertson-Walker spaces. The primary string constraints are found to be split into a chain of perturbative constraints and their conservation and consistency are proved. It is established that in the proposed realization of the perturbative approach the string dynamics in the de Sitter space is stable for a large Hubble constant $H (\alpha^{\prime}H^{2}\gg1)$.