Stretched quantum membranes

TL;DR

This paper investigates stretched bosonic and supersymmetric membranes, establishing their equivalence to string-like configurations through perturbation theory, and determines their quantum mass spectrum with critical dimensions 27 and 11.

Contribution

It introduces a perturbative approach around zero-tension configurations, proving their equivalence to string-like states and analyzing their quantum properties and spectra.

Findings

Membrane configurations are canonically equivalent to string-like configurations.

Quantum analysis shows a critical dimension of 27 for bosonic and 11 for supersymmetric cases.

The mass spectrum is discrete, with a string-like ground state and split excited states.

Abstract

We study bosonic and space-time supersymmetric membranes with small tensions corresponding to stretched configurations. Using a generalized lightcone gauge, one may set up a perturbation theory around configurations having zero tension. We will show, by explicit construction to all orders in perturbation theory, that these membrane configurations are canonically equivalent, and thereby solvable, to string-like configurations with string excitations transverse to the stretched direction. At the quantum level, it is shown that there exists an ordering such that equivalence by unitary transformations is achieved. Consistency requires the critical dimensions 27 and 11 for the bosonic and supersymmetric cases, respectively. The mass spectrum is determined to any order. It is discrete and contains massless exitations. The ground state is purely string-like, whereas excited string-like states split through the perturbation into an infinite set of states with equal or lower energies.