BRST Formulation of 4-Monopoles

TL;DR

This paper develops a BRST-based topological field theory for 4-monopoles on Riemannian manifolds, ensuring off-shell supersymmetry and a novel canonical approach using Morse functions.

Contribution

It introduces a new BRST formulation for 4-monopoles that includes auxiliary and Wess-Zumino fields naturally, with a canonical approach based on Morse functions.

Findings

Constructed a supersymmetric gauge invariant action for 4-monopoles.

Achieved off-shell closure of the topological supersymmetric algebra.

Developed a canonical approach using Morse functions and BRST boundary conditions.

Abstract

A supersymmetric gauge invariant action is constructed over any 4-dimensional Riemannian manifold describing Witten's theory of 4-monopoles. The topological supersymmetric algebra closes off-shell. The multiplets include the auxiliary fields and the Wess-Zumino fields in an unusual way, arising naturally from BRST gauge fixing. A new canonical approach over Riemann manifolds is followed, using a Morse function as an euclidean time and taking into account the BRST boundary conditions that come from the BFV formulation. This allows a construction of the effective action starting from gauge principles.