Gauge field fluctuation corrected QED3 effective action by fermionic particle-vortex duality

Abstract

We present a non-perturbative framework for incorporating gauge field fluctuations into effective actions of QED3 in the infrared using fermionic particle-vortex duality. This approach is demonstrated through the applications to models containing N species of 2-component Dirac fermions in solvable and interpretable electromagnetic backgrounds, focusing on N = 1 or 2. For the N = 1 model, we establish a correspondence between fermion Casimir energy at finite density and the magnetic Euler-Heisenberg Lagrangian, and further evaluate the corrections to their amplitudes. This predicts amplification of charge susceptibility and reduction of magnetic permeability. We additionally provide physical interpretations for each component of our calculation and offer alternative derivations based on energy density measurements in different characteristic lengths. For N = 2, we show that magnetic catalysis is erased in a U(1) × U(1) QED3, indicating no breakdown of chiral symmetry. Reasoning is offered based on the properties of the lowest Landau level wave functions.