An Exact Membrane Quantization from W(Infinity) Symmetry

TL;DR

This paper presents an exact quantization method for spherical membranes in flat spacetime using $W_{inity}$ symmetry and integrable Toda equations, revealing both continuous and discrete energy spectra and linking membrane solutions to singleton field theory.

Contribution

It introduces a novel exact quantization approach for membranes based on $W_{inity}$ symmetry and integrability, providing explicit solutions and energy spectra.

Findings

Continuous and discrete energy levels identified.

Membrane wavefunctionals expressed via Bessel functions.

Potential connections to singleton field theory outlined.

Abstract

An exact quantization of the spherical membrane moving in flat target spacetime backgrounds is performed. Crucial ingredients are the exact integrabilty of the $3D~SU(\infty)$ continuous Toda equation and the quasi-finite highest weight irreducible representations of $W_{\infty}$ algebras. Both continuous and discrete energy levels are found. The latter are found for periodic-like solutions. Membrane wavefunctionals solutions are found in terms of Bessel's functions and plausible relations to singleton field theory are outlined.