Dimension of the moduli space and Hamiltonian analysis of BF field theories

TL;DR

This paper calculates the dimension of the moduli space for BF theories in 2D and 4D using Atiyah-Singer theorem and develops a Hamiltonian analysis for a modified 4D BF theory related to topological Yang-Mills theory.

Contribution

It introduces a method to determine moduli space dimensions for BF theories and provides a Hamiltonian framework for a modified 4D BF theory, linking it to topological YM.

Findings

Moduli space dimension formulas for BF theories in various dimensions.

Hamiltonian analysis framework for a modified BF theory.

Connection between BF theories and topological Yang-Mills theory.

Abstract

By using the Atiyah-Singer theorem through some similarities with the instanton and the anti-instanton moduli spaces, the dimension of the moduli space for two and four-dimensional BF theories valued in different background manifolds and gauge groups scenarios is determined. Additionally, we develop Dirac's canonical analysis for a four-dimensional modified BF theory, which reproduces the topological YM theory. This framework will allow us to understand the local symmetries, the constraints, the extended Hamiltonian and the extended action of the theory.