Spinning branes in Riemann-Cartan spacetime

TL;DR

This paper investigates the motion of spinning branes in Riemann-Cartan spacetime, revealing new spin-curvature couplings and relating the Kalb-Ramond field to torsion, with implications for string and particle dynamics.

Contribution

It derives covariant world-sheet equations for spinning branes in Riemann-Cartan geometry, uncovering novel spin-curvature interactions and clarifying the geometric role of the Kalb-Ramond field.

Findings

Zero-size particle spin does not couple to background curvature.

String dynamics show coupling to the Kalb-Ramond field as torsion.

New covariant equations for brane motion in Riemann-Cartan spacetime.

Abstract

We use the conservation law of the stress-energy and spin tensors to study the motion of massive brane-like objects in Riemann-Cartan geometry. The world-sheet equations and boundary conditions are obtained in a manifestly covariant form. In the particle case, the resultant world-line equations turn out to exhibit a novel spin-curvature coupling. In particular, the spin of a zero-size particle does not couple to the background curvature. In the string case, the world-sheet dynamics is studied for some special choices of spin and torsion. As a result, the known coupling to the Kalb-Ramond antisymmetric external field is obtained. Geometrically, the Kalb-Ramond field has been recognized as a part of the torsion itself, rather than the torsion potential.