Test membranes in Riemann-Cartan spacetimes

Abstract

The dynamics of brane-like extended objects in spacetimes with torsion is derived from the conservation equations of stress-energy and spin tensors. Thus obtained world-sheet equations are applied to macroscopic test membranes made of spinning matter. Specifically, we consider membranes with maximally symmetric distribution of stress-energy and spin. These are characterized by two constants only: the tension and spin magnitude. By solving the world-sheet equations, we discover a similarity between such membranes in Riemann-Cartan backgrounds, and string theory membranes in low-energy string backgrounds. In the second part of the paper, we apply this result to cylindrical membranes wrapped around the extra compact dimension of a $(D+1)$-dimensional spacetime. In the narrow membrane limit, we discover how effective macroscopic strings couple to torsion. An observed similarity with the string sigma model is noted.

v2: Published version. Text completely rewritten.

References in corpus (3)

• Classical Spinning Branes in Curved Backgrounds
• Classical String in Curved Backgrounds
• Spinning branes in Riemann-Cartan spacetime

Cited by in corpus (2)

• Entanglement-induced deviation from the geodesic motion in quantum gravity
• String background fields and Riemann-Cartan geometry