Five-Dimensional BF Theory and Four-Dimensional Current Algebra

TL;DR

This paper explores the connection between a five-dimensional BF topological field theory and a four-dimensional current algebra, demonstrating an exact solvability through axial gauge fixing in a perturbative quantum field theory framework.

Contribution

It introduces a method to relate five-dimensional BF theory to four-dimensional current algebra using axial gauge fixing, enabling exact solutions.

Findings

The theory is well-defined after axial gauge fixing.

The model can be solved exactly.

A clear relation between 5D BF theory and 4D current algebra is established.

Abstract

We consider the relation between the five-dimensional BF model and a four-dimensional local current algebra from the point of view of perturbative local quantum field theory. We use an axial gauge fixing procedure and show that it allows for a well defined theory which actually can be solved exactly.