Functional determinant and Green functions for a fermionic gauge theory on the disk

TL;DR

This paper calculates the functional determinant and Green functions for Dirac fermions on a disk with an electromagnetic field, analyzing the associated coset model and its correlation functions.

Contribution

It introduces a method to compute the functional determinant and Green functions for fermions in a gauge theory on a disk, including boundary conditions and coset model analysis.

Findings

Computed the functional determinant after decoupling gauge degrees of freedom.

Derived Green functions with boundary conditions.

Analyzed the coset model and its correlation functions.

Abstract

We study a theory of Dirac fermions on a disk in presence of an electromagnetic field. Using the heat-kernel technique we compute the functional determinant which results after decoupling the zero-flux gauge degrees of freedom from the fermions. We also compute the Green functions of the remaining fermionic theory with the appropriate boundary conditions. Finally we analyze the coset model associated to this gauge theory and compute all its correlations functions.