On a Lorentz covariant matrix regularization of membrane theories

TL;DR

This paper develops a Lorentz covariant matrix regularization method for bosonic membranes, preserving gauge symmetries and discussing potential extensions to supermembranes, advancing the theoretical understanding of membrane quantization.

Contribution

It introduces a Lorentz covariant matrix regularization framework for bosonic membranes, maintaining gauge symmetries and addressing reparametrization issues.

Findings

Matrix regularization defines membrane action covariantly.

Area preserving diffeomorphism generator is consistent.

Reparametrization BRST charge depends on basis choice.

Abstract

A Lorentz covariant matrix regularization of membrane thories is studied.It is shown that the action for a bosonic membrane can be defined by matrix regularization in a Lorentz covariant manner. The generator of area preserving diffeomorphism can also be consistently defined by matrix regularization, and we can make the area preserving gauge symmetry manifest. However, the reparametrization BRST charge explicitly depends on a specific basis set introduced to define the matrix regularization. We also briefly comment on an extension of the present formulation to a supermembrane.