Mass-Gaps and Spin Chains for (Super) Membranes

TL;DR

This paper introduces a method to compute the non-perturbative mass gap in bosonic membrane theories using matrix regularization, large N perturbation theory, and quantum spin chains, applicable to flat and plane wave spacetimes.

Contribution

It develops a novel approach linking mass-gap calculations with spin chain models and extends analysis to non-critical membranes in plane wave backgrounds.

Findings

Mass gap computed via matrix regularization and expansion in 1/d.

Large N perturbation theory developed around effective potentials.

One-loop spectra obtained using Bethe ansatz for various models.

Abstract

We present a method for computing the non-perturbative mass-gap in the theory of Bosonic membranes in flat background spacetimes with or without background fluxes. The computation of mass-gaps is carried out using a matrix regularization of the membrane Hamiltonians. The mass gap is shown to be naturally organized as an expansion in a 'hidden' parameter, which turns out to be $\frac{1}{d}$: d being the related to the dimensionality of the background space. We then proceed to develop a large $N$ perturbation theory for the membrane/matrix-model Hamiltonians around the quantum/mass corrected effective potential. The same parameter that controls the perturbation theory for the mass gap is also shown to control the Hamiltonian perturbation theory around the effective potential. The large $N$ perturbation theory is then translated into the language of quantum spin chains and the one loop spectra of various Bosonic matrix models are computed by applying the Bethe ansatz to the one-loop effective Hamiltonians for membranes in flat space times. Apart from membranes in flat spacetimes, the recently proposed matrix models (hep-th/0607005) for non-critical membranes in plane wave type spacetimes are also analyzed within the paradigm of quantum spin chains and the Bosonic sectors of all the models proposed in (hep-th/0607005) are diagonalized at the one-loop level.