# Non-cancellation of the parity anomaly in the strong-field regime of QED$_{2+1}$

## TL;DR

This paper demonstrates that quantum anomalies in 2+1 dimensional QED lead to observable effects in strong electric fields, with both analytical and numerical evidence highlighting their significance in various physical contexts.

## Contribution

It reveals a non-cancellation of the parity anomaly in strong fields through analytical solutions and lattice simulations, emphasizing its importance in condensed matter and high-energy physics.

## Key findings

- Non-cancellation of the parity anomaly in strong electric fields
- Analytical solutions in the static field limit
- Lattice simulation results confirming anomaly effects

## Abstract

Quantum fluctuations lead to an anomalous violation of parity symmetry in quantum electrodynamics for an even number of spatial dimensions. While the leading parity-odd electric current vanishes in vacuum, we uncover a non-cancellation of the anomaly for strong electric fields with distinct macroscopic signatures. We perform real-time lattice simulations with fully dynamical gauge fields and Wilson fermions in $2+1$ space-time dimensions. In the static field limit, relevant at early times, we solve the problem analytically. Our results point out the fundamental role of quantum anomalies for strong-field phenomena, relevant for a wide range of condensed matter and high-energy applications, but also for the next generation of gauge theory quantum simulators.