The supermembrane with winding

TL;DR

This paper explores how wrapping supermembranes around compact dimensions introduces central charges in the supersymmetry algebra, affecting their mass spectrum and BPS states while maintaining Lorentz invariance.

Contribution

It demonstrates the consistency of central charges with Lorentz symmetry and analyzes their impact on the supermembrane's mass spectrum and BPS states.

Findings

Central charges arise from membrane wrapping around compact dimensions.

Mass spectrum remains continuous despite the presence of central charges.

Lower mass bound is determined by winding number, corresponding to BPS states.

Abstract

The supersymmetry algebra for supermembranes, quantized in the light-cone gauge, exhibits central charges induced by wrapping the membrane around compact dimensions. These central charges are manifestly consistent with Lorentz symmetry. While the central charges raise the mass of the membrane states, they still leave the mass spectrum continuous, at least generically. The lower bound on the mass spectrum is set by the winding number and corresponds to a BPS state.