Exact String Solutions in Nontrivial Backgrounds

TL;DR

This paper develops methods to find exact solutions for classical string and D1-brane dynamics in complex gravity backgrounds, including Kalb-Ramond fields, by reducing the problem to constrained particle motion and providing explicit examples.

Contribution

It introduces sufficient conditions for exact solutions of string equations in nontrivial backgrounds, extending to D1-branes and tensionless strings, with practical examples across dimensions.

Findings

Derived conditions for exact string solutions in gravity backgrounds.

Extended analysis to include Kalb-Ramond fields.

Found explicit solutions for D1-branes and tensionless strings.

Abstract

We show how the classical string dynamics in $D$-dimensional gravity background can be reduced to the dynamics of a massless particle constrained on a certain surface whenever there exists at least one Killing vector for the background metric. We obtain a number of sufficient conditions, which ensure the existence of exact solutions to the equations of motion and constraints. These results are extended to include the Kalb-Ramond background. The $D1$-brane dynamics is also analyzed and exact solutions are found. Finally, we illustrate our considerations with several examples in different dimensions. All this also applies to the tensionless strings.