String background fields and Riemann-Cartan geometry

TL;DR

This paper explores how cylindrical membranes in a Riemann-Cartan spacetime relate to effective string theories, revealing a connection between background fields and spacetime geometry.

Contribution

It derives membrane dynamics from conservation laws and shows their reduction to string-like models with background fields linked to spacetime geometry.

Findings

Membrane equations derived from stress-energy and spin conservation.

Dimensional reduction yields effective string coupling to geometry.

Identifies correspondence between string background fields and Riemann-Cartan spacetime features.

Abstract

We study classical dynamics of cylindrical membranes wrapped around the extra compact dimension of a $(D+1)$-dimensional Riemann-Cartan spacetime. The world-sheet equations and boundary conditions are obtained from the universally valid conservation equations of the stress-energy and spin tensors. Specifically, we consider membranes made of macroscopic matter with maximally symmetric distribution of spin. In the narrow membrane limit, the dimensionally reduced theory is obtained. It describes how effective strings couple to the effective $D$-dimensional geometry. The striking coincidence with the string theory $\sigma$-model is observed. In this correspondence, the string background fields $G_{\mu\nu}$, $B_{\mu\nu}$, $A_{\mu}$ and $\Phi$ are related to the metric and torsion of the Riemann-Cartan spacetime.