# Flavor and topological current correlators in parity-invariant three-dimensional QED

## TL;DR

This study uses lattice regularization to analyze how flavor-triplet fermion current correlators evolve from free-field behavior to conformal invariance in parity-invariant 3D QED, revealing symmetry enhancement and the importance of fermion dynamics.

## Contribution

It provides the first numerical evidence supporting the degeneracy of flavor and topological current correlators and the role of fermions in scale invariance in 3D QED.

## Key findings

- Flavor-triplet fermion current approaches conformal value in IR
- Degeneracy of flavor and topological currents supports O(4) symmetry
- Fermion dynamics are essential for scale invariance

## Abstract

We use lattice regularization to study the flow of the flavor-triplet fermion current central charge $C^f_J$ from its free field value in the ultraviolet limit to its conformal value in the infrared limit of the parity-invariant three-dimensional QED with two flavors of two-component fermions. The dependence of $C^f_J$ on the scale is weak with a tendency to be below the free field value at intermediate distances. Our numerical data suggests that the flavor-triplet fermion current and the topological current correlators become degenerate within numerical errors in the infra-red limit, thereby supporting an enhanced O(4) symmetry predicted by strong self-duality. Further, we demonstrate that fermion dynamics is necessary for the scale-invariant behavior of parity-invariant three-dimensional QED by showing that the pure gauge theory with non-compact gauge action has non-zero bilinear condensate.