Classical membrane in a time dependent orbifold

TL;DR

This paper studies the classical dynamics of membranes in singular, time-dependent backgrounds, showing their equivalence to string theories in curved spacetimes, with implications for quantum membrane theories.

Contribution

It demonstrates the classical equivalence of membranes winding around compact dimensions to strings in curved spacetime, providing a foundation for quantum membrane analysis in Milne space.

Findings

Membrane dynamics are governed by first-class constraints.

Membrane winding leads to a string-like description in curved spacetime.

Results facilitate future quantum membrane formulations.

Abstract

We analyze classical theory of a membrane propagating in a singular background spacetime. The algebra of the first-class constraints of the system defines the membrane dynamics. A membrane winding uniformly around compact dimension of embedding spacetime is described by two constraints, which are interpreted in terms of world-sheet diffeomorhisms. The system is equivalent to a closed bosonic string propagating in a curved spacetime. Our results may be used for finding a quantum theory of a membrane in the compactified Milne space.