Exact Brane Solutions in Curved Backgrounds

TL;DR

This paper develops a method for solving null p-brane equations in curved backgrounds with at least one Killing vector, providing explicit solutions and applying BRST quantization techniques.

Contribution

It introduces a new approach for solving tensionless p-brane equations in curved spaces with Killing vectors, extending to tensile 1-branes and providing explicit solutions.

Findings

Method for solving tensionless p-brane equations developed

Explicit exact solutions provided in four-dimensional backgrounds

Applicable to both null and tensile 1-branes

Abstract

We consider the classical null p-brane dynamics in D-dimensional curved backgrounds and apply the Batalin-Fradkin-Vilkovisky approach for BRST quantization of general gauge theories. Then we develop a method for solving the tensionless $p$-brane equations of motion and constraints. This is possible whenever there exists at least one Killing vector for the background metric. It is shown that the same method can be also applied for the tensile 1-branes. Finally, we give two examples of explicit exact solutions in four dimensions.