Test membranes in Riemann-Cartan spacetimes

TL;DR

This paper derives the dynamics of test membranes with spin in Riemann-Cartan spacetimes, revealing similarities to string theory and exploring their coupling to torsion, with potential implications for higher-dimensional theories.

Contribution

It introduces world-sheet equations for spinning membranes in torsionful spacetimes and uncovers their relation to string theory in low-energy backgrounds.

Findings

Membranes with symmetric stress-energy and spin characterized by tension and spin magnitude.

Similarity between membranes in Riemann-Cartan backgrounds and string theory membranes.

Effective coupling of macroscopic strings to torsion in compactified dimensions.

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.