Master Canonical Action and BRST Charge of the M Theory Bosonic Five Brane

TL;DR

This paper provides a comprehensive canonical analysis of the gauge-fixed PST bosonic five brane, constructs the BRST charge, and explores the Hamiltonian structure and constraints without assuming the inverse metric, revealing physical configurations and stability.

Contribution

It introduces a master canonical action with only first class constraints for the bosonic five brane and constructs the nilpotent BRST charge without requiring the inverse metric, advancing the understanding of its canonical structure.

Findings

Constructed the BRST charge and invariant theory.

Identified the Hamiltonian and analyzed stability.

Characterized the Hamiltonian constraint algebra.

Abstract

A complete analysis of the canonical structure for a gauge fixed PST bosonic five brane action is performed. This canonical formulation is quadratic in the dependence on the antisymmetric field and it has second class constraints. We remove the second class constraints and a master canonical action with only first class constraints is proposed. The nilpotent BRST charge and its BRST invariant effective theory is constructed. The construction does not assume the existence of the inverse of the induced metric. Singular configurations are then physical ones. We obtain the physical Hamiltonian of the theory and analyze its stability properties. Finally, by studying the algebra of diffeomorphisms we find under mild assumptions the general structure for the Hamiltonian constraint for theories invariant under 6 dimensional diffeomorphisms and we give an algebraic characterization of the constraint associated with the bosonic five brane action. We also identify the constraint for the bosonic five brane action upgraded with a cosmological term, it contains a Born-Infeld type term.