Classical Spinning Branes in Curved Backgrounds

TL;DR

This paper derives the covariant equations of motion for classical spinning branes in curved backgrounds, revealing how intrinsic angular momentum interacts with curvature and boundary conditions, with detailed analysis of particles and strings.

Contribution

It introduces a covariant framework for spinning branes in curved spacetime, including boundary conditions and gauge symmetries, extending previous models to incorporate intrinsic angular momentum.

Findings

Intrinsic angular momentum couples to background curvature.

Derived covariant world sheet equations and boundary conditions.

Analyzed spinning particles and strings in four dimensions.

Abstract

The dynamics of a classical branelike object in a curved background is derived from the covariant stress-energy conservation of the brane matter. The world sheet equations and boundary conditions are obtained in the pole-dipole approximation, where nontrivial brane thickness gives rise to its intrinsic angular momentum. It is shown that intrinsic angular momentum couples to both, the background curvature and the brane orbital degrees of freedom. The whole procedure is manifestly covariant with respect to spacetime diffeomorphisms and world sheet reparametrizations. In addition, two extra gauge symmetries are discovered and utilized. The examples of the point particle and the string in 4 spacetime dimensions are analyzed in more detail. A particular attention is paid to the Nambu-Goto string with massive spinning particles attached to its ends.